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7 |
#
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| 8 |
8 |
# Documentation by Kevin Jackson and Gavin Sinclair.
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| 9 |
9 |
#
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10 |
# Performance improvements by Kurt Stephens.
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11 |
#
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| 10 |
12 |
# When you <tt>require 'rational'</tt>, all interactions between numbers
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| 11 |
13 |
# potentially return a rational result. For example:
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14 |
#
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| ... | ... | |
| 104 |
106 |
num = -num
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107 |
den = -den
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| 106 |
108 |
end
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| 107 |
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if num.kind_of?(Integer) and den.kind_of?(Integer)
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| 108 |
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@numerator = num
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| 109 |
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@denominator = den
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| 110 |
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else
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| 111 |
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@numerator = num.to_i
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| 112 |
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@denominator = den.to_i
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| 113 |
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end
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109 |
@numerator = num.to_i
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110 |
@denominator = den.to_i
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111 |
end
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112 |
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#
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| ... | ... | |
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119 |
# r + 0.5 # -> 1.25
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120 |
#
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121 |
def + (a)
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if a.kind_of?(Rational)
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num = @numerator * a.denominator
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num_a = a.numerator * @denominator
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Rational(num + num_a, @denominator * a.denominator)
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elsif a.kind_of?(Integer)
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self + Rational.new!(a, 1)
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elsif a.kind_of?(Float)
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Float(self) + a
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122 |
case a
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123 |
when Rational # => Rational | Integer
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124 |
Rational( (@numerator * a.denominator) + (a.numerator * @denominator), @denominator * a.denominator)
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125 |
when Integer # => Rational
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126 |
Rational.reduce((@numerator ) + (a * @denominator), @denominator)
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127 |
when Float
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128 |
self.to_f + a
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129 |
else
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130 |
x, y = a.coerce(self)
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131 |
x + y
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| ... | ... | |
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142 |
# r - 0.5 # -> 0.25
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143 |
#
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144 |
def - (a)
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if a.kind_of?(Rational)
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num = @numerator * a.denominator
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num_a = a.numerator * @denominator
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Rational(num - num_a, @denominator*a.denominator)
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| 153 |
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elsif a.kind_of?(Integer)
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self - Rational.new!(a, 1)
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elsif a.kind_of?(Float)
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Float(self) - a
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145 |
case a
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146 |
when Rational # => Rational | Integer
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147 |
Rational( (@numerator * a.denominator) - (a.numerator * @denominator), @denominator * a.denominator)
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148 |
when Integer # => Rational
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149 |
Rational.reduce((@numerator ) - (a * @denominator), @denominator)
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150 |
when Float
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151 |
self.to_f - a
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152 |
else
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153 |
x, y = a.coerce(self)
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154 |
x - y
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| ... | ... | |
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156 |
end
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157 |
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#
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159 |
# Unary Minus--Returns the receiver's value, negated.
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#
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def -@
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162 |
Rational.new!(- @numerator, @denominator)
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163 |
end
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#
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# Returns the product of this value and +a+.
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#
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168 |
# Examples:
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| ... | ... | |
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173 |
# r * Rational(1,2) # -> Rational(3,8)
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#
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175 |
def * (a)
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if a.kind_of?(Rational)
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num = @numerator * a.numerator
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den = @denominator * a.denominator
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Rational(num, den)
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elsif a.kind_of?(Integer)
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self * Rational.new!(a, 1)
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elsif a.kind_of?(Float)
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Float(self) * a
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case a
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when Rational
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Rational(@numerator * a.numerator, @denominator * a.denominator)
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when Integer
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180 |
Rational(@numerator * a , @denominator)
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when Float
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182 |
self.to_f * a
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183 |
else
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184 |
x, y = a.coerce(self)
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185 |
x * y
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| ... | ... | |
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194 |
# r / Rational(1,2) # -> Rational(3,2)
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#
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196 |
def / (a)
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| 196 |
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if a.kind_of?(Rational)
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num = @numerator * a.denominator
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den = @denominator * a.numerator
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Rational(num, den)
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| 200 |
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elsif a.kind_of?(Integer)
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197 |
case a
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198 |
when Rational
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199 |
Rational(@numerator * a.denominator, @denominator * a.numerator)
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200 |
when Integer
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201 |
raise ZeroDivisionError, "division by zero" if a == 0
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| 202 |
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self / Rational.new!(a, 1)
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| 203 |
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elsif a.kind_of?(Float)
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Float(self) / a
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202 |
Rational(@numerator , @denominator * a )
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203 |
when Float
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204 |
self.to_f / a
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205 |
else
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206 |
x, y = a.coerce(self)
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207 |
x / y
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| ... | ... | |
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218 |
# r ** Rational(1,2) # -> 0.866025403784439
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219 |
#
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220 |
def ** (other)
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| 221 |
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if other.kind_of?(Rational)
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| 222 |
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Float(self) ** other
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| 223 |
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elsif other.kind_of?(Integer)
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221 |
case other
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when Rational, Float
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223 |
self.to_f ** other
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224 |
when Integer
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| 224 |
225 |
if other > 0
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num = @numerator ** other
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| 226 |
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den = @denominator ** other
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226 |
Rational.new!(@numerator ** other, @denominator ** other)
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| 227 |
227 |
elsif other < 0
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| 228 |
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num = @denominator ** -other
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| 229 |
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den = @numerator ** -other
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| 230 |
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elsif other == 0
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num = 1
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| 232 |
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den = 1
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228 |
Rational.new!(@denominator ** -other, @numerator ** -other)
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229 |
else
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230 |
Rational.new!(1, 1) # why not Fixnum 1?
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| 233 |
231 |
end
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| 234 |
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Rational.new!(num, den)
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| 235 |
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elsif other.kind_of?(Float)
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Float(self) ** other
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| 237 |
232 |
else
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| 238 |
233 |
x, y = other.coerce(self)
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| 239 |
234 |
x ** y
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| ... | ... | |
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251 |
#
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| 257 |
252 |
def % (other)
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| 258 |
253 |
value = (self / other).floor
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| 259 |
|
return self - other * value
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254 |
self - other * value
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| 260 |
255 |
end
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| 261 |
256 |
|
| 262 |
257 |
#
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| ... | ... | |
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263 |
#
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| 269 |
264 |
def divmod(other)
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| 270 |
265 |
value = (self / other).floor
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| 271 |
|
return value, self - other * value
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266 |
[ value, self - other * value ]
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| 272 |
267 |
end
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| 273 |
268 |
|
| 274 |
269 |
#
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| ... | ... | |
| 282 |
277 |
end
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| 283 |
278 |
end
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| 284 |
279 |
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280 |
# Returns true or false.
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281 |
def zero?
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282 |
@numerator.zero?
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283 |
end
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284 |
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285 |
# See Numeric#nonzero?
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286 |
def nonzero?
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|
287 |
@numerator.nonzero? ? self : nil
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|
288 |
end
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289 |
|
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290 |
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| 285 |
291 |
#
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| 286 |
292 |
# Returns +true+ iff this value is numerically equal to +other+.
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| 287 |
293 |
#
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| ... | ... | |
| 292 |
298 |
# Don't use Rational.new!
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| 293 |
299 |
#
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| 294 |
300 |
def == (other)
|
| 295 |
|
if other.kind_of?(Rational)
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|
301 |
case other
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|
302 |
when Rational
|
| 296 |
303 |
@numerator == other.numerator and @denominator == other.denominator
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| 297 |
|
elsif other.kind_of?(Integer)
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| 298 |
|
self == Rational.new!(other, 1)
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| 299 |
|
elsif other.kind_of?(Float)
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| 300 |
|
Float(self) == other
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|
304 |
when Integer
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|
305 |
@numerator == other && @denominator == 1
|
|
306 |
when Float
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|
307 |
self.to_f == other
|
| 301 |
308 |
else
|
| 302 |
309 |
other == self
|
| 303 |
310 |
end
|
| ... | ... | |
| 307 |
314 |
# Standard comparison operator.
|
| 308 |
315 |
#
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| 309 |
316 |
def <=> (other)
|
| 310 |
|
if other.kind_of?(Rational)
|
| 311 |
|
num = @numerator * other.denominator
|
| 312 |
|
num_a = other.numerator * @denominator
|
| 313 |
|
v = num - num_a
|
| 314 |
|
if v > 0
|
| 315 |
|
return 1
|
| 316 |
|
elsif v < 0
|
| 317 |
|
return -1
|
| 318 |
|
else
|
| 319 |
|
return 0
|
| 320 |
|
end
|
| 321 |
|
elsif other.kind_of?(Integer)
|
| 322 |
|
return self <=> Rational.new!(other, 1)
|
| 323 |
|
elsif other.kind_of?(Float)
|
| 324 |
|
return Float(self) <=> other
|
| 325 |
|
elsif defined? other.coerce
|
| 326 |
|
x, y = other.coerce(self)
|
| 327 |
|
return x <=> y
|
|
317 |
case other
|
|
318 |
when Rational
|
|
319 |
((@numerator * other.denominator) <=> (other.numerator * @denominator))
|
|
320 |
when Integer
|
|
321 |
((@numerator ) <=> (other * @denominator))
|
|
322 |
when Float
|
|
323 |
self.to_f <=> other
|
| 328 |
324 |
else
|
| 329 |
|
return nil
|
|
325 |
if defined? other.coerce
|
|
326 |
x, y = other.coerce(self)
|
|
327 |
x <=> y
|
|
328 |
end # nil
|
| 330 |
329 |
end
|
| 331 |
330 |
end
|
| 332 |
331 |
|
| 333 |
332 |
def coerce(other)
|
| 334 |
|
if other.kind_of?(Float)
|
| 335 |
|
return other, self.to_f
|
| 336 |
|
elsif other.kind_of?(Integer)
|
| 337 |
|
return Rational.new!(other, 1), self
|
|
333 |
case other
|
|
334 |
when Float
|
|
335 |
[ other, self.to_f ]
|
|
336 |
when Integer
|
|
337 |
[ Rational.new!(other, 1), self ]
|
| 338 |
338 |
else
|
| 339 |
339 |
super
|
| 340 |
340 |
end
|
| ... | ... | |
| 363 |
363 |
|
| 364 |
364 |
def truncate()
|
| 365 |
365 |
if @numerator < 0
|
| 366 |
|
return -((-@numerator).div(@denominator))
|
|
366 |
-((-@numerator).div(@denominator))
|
|
367 |
else
|
|
368 |
@numerator.div(@denominator)
|
| 367 |
369 |
end
|
| 368 |
|
@numerator.div(@denominator)
|
| 369 |
370 |
end
|
| 370 |
371 |
|
| 371 |
372 |
alias_method :to_i, :truncate
|
| 372 |
373 |
|
| 373 |
374 |
def round()
|
| 374 |
375 |
if @numerator < 0
|
| 375 |
|
num = -@numerator
|
| 376 |
|
num = num * 2 + @denominator
|
| 377 |
|
den = @denominator * 2
|
| 378 |
|
-(num.div(den))
|
|
376 |
-((@numerator * -2 + @denominator).div(@denominator * 2))
|
| 379 |
377 |
else
|
| 380 |
|
num = @numerator * 2 + @denominator
|
| 381 |
|
den = @denominator * 2
|
| 382 |
|
num.div(den)
|
|
378 |
((@numerator * 2 + @denominator).div(@denominator * 2))
|
| 383 |
379 |
end
|
| 384 |
380 |
end
|
| 385 |
381 |
|
| ... | ... | |
| 401 |
397 |
if @denominator == 1
|
| 402 |
398 |
@numerator.to_s
|
| 403 |
399 |
else
|
| 404 |
|
@numerator.to_s+"/"+@denominator.to_s
|
|
400 |
"#{@numerator}/#{@denominator}"
|
| 405 |
401 |
end
|
| 406 |
402 |
end
|
| 407 |
403 |
|
| ... | ... | |
| 418 |
414 |
# Rational(5,8).inspect # -> "Rational(5, 8)"
|
| 419 |
415 |
#
|
| 420 |
416 |
def inspect
|
| 421 |
|
sprintf("Rational(%s, %s)", @numerator.inspect, @denominator.inspect)
|
|
417 |
"Rational(#{@numerator.inspect}, #{@denominator.inspect})"
|
| 422 |
418 |
end
|
| 423 |
419 |
|
| 424 |
420 |
#
|