Rational

Tadayoshi_F · April 12, 2006, 6:56pm

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In message “Re: [ruby-dev:28551] Re: Rational”
on Thu, 13 Apr 2006 01:34:51 +0900, Shin-ichiro HARA
[email protected] writes:

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Tadayoshi_F · April 13, 2006, 3:33am

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Tadayoshi_F · April 13, 2006, 4:47am

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Tadayoshi_F · April 13, 2006, 5:05am

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In message “Re: [ruby-dev:28558] Re: Rational”
on Thu, 13 Apr 2006 11:46:29 +0900, Shin-ichiro HARA
[email protected] writes:

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Tadayoshi_F · April 13, 2006, 3:58am

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In message “Re: [ruby-dev:28556] Re: Rational”
on Thu, 13 Apr 2006 10:31:57 +0900, Shin-ichiro HARA
[email protected] writes:

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Tadayoshi_F · April 13, 2006, 6:11am

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Tadayoshi_F · April 15, 2006, 7:35pm

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Tadayoshi_F · April 15, 2006, 7:25pm

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class Float
def decode
f, e = Math.frexp(self)
[Math.ldexp(f, Float::MANT_DIG).floor, e - Float::MANT_DIG]
end
end

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def rationalize(r, e = nil)
return(-rationalize(-r, e)) if r < 0
if e
raise ArgumentError, “negative precision” if e < 0
x = Rational(r - e)
y = Rational(r + e)

return x if x == y

xn, xd = x.numerator, x.denominator
yn, yd = y.numerator, y.denominator

else
f0, e0 = r.decode

return f0 << e0 if e0 >= 0

xn, xd = 2*f0 - 1, 1 << (1 - e0)
yn, yd = 2*f0 + 1, 1 << (1 - e0)

end

a, b, c, d = 1, 0, 0, 1
while true
xq, xr = xn.divmod(xd)
yq, yr = yn.divmod(yd)

if xr.zero?
  return Rational(a*xq + b, c*xq + d)
elsif xq < yq
  return Rational(a*(xq + 1) + b, c*(xq + 1) + d)
elsif xq > yq
  raise "implementation error"
end

a, b, c, d = a*xq + b, a, c*xq + d, c
xn, xd, yn, yd = yd, yr, xd, xr

end
end

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class Float
def -(y)
(rationalize - y.rationalize).to_f
end
end

p 61.1 - 60.0 == 1.1 #=> true

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Tadayoshi_F · April 16, 2006, 2:32am

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