Module: Rationalize

Extended by:
CMath
Includes:
CMath
Defined in:
lib/rationalize.rb

Overview

Rationalize is a refinement version of mathn.

Examples:


p 1 / 3 #=> 0
class Foo
  using Rationalize
  p 1 / 3 #=> (1/3)
end
p 1 / 3 #=> 0
p Rationalize.sqrt(Rational(9, 4)) #=> (3/2)

Class Method Summary collapse

Class Method Details

.rsqrt(a) ⇒ Object 



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# File 'lib/rationalize.rb', line 157

def rsqrt(a)
  if a.kind_of?(Float)
    sqrt!(a)
  elsif a.kind_of?(Rational)
    rsqrt(a.numerator)/rsqrt(a.denominator)
  else
    src = a
    max = 2 ** 32
    byte_a = [src & 0xffffffff]
    # ruby's bug
    while (src >= max) and (src >>= 32)
      byte_a.unshift src & 0xffffffff
    end

    answer = 0
    main = 0
    side = 0
    for elm in byte_a
      main = (main << 32) + elm
      side <<= 16
      if answer != 0
        if main * 4  < side * side
          applo = main.div(side)
        else
          applo = ((sqrt!(side * side + 4 * main) - side)/2.0).to_i + 1
        end
      else
        applo = sqrt!(main).to_i + 1
      end

      while (x = (side + applo) * applo) > main
        applo -= 1
      end
      main -= x
      answer = (answer << 16) + applo
      side += applo * 2
    end
    if main == 0
      answer
    else
      sqrt!(a)
    end
  end
end

.sqrt(a) ⇒ Object 



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# File 'lib/rationalize.rb', line 132

def sqrt(a)
  if a.kind_of?(Complex)
    abs = sqrt(a.real*a.real + a.imag*a.imag)
#      if not abs.kind_of?(Rational)
#        return a**Rational(1,2)
#      end
    x = sqrt((a.real + abs)/Rational(2))
    y = sqrt((-a.real + abs)/Rational(2))
#      if !(x.kind_of?(Rational) and y.kind_of?(Rational))
#        return a**Rational(1,2)
#      end
    if a.imag >= 0
      Complex(x, y)
    else
      Complex(x, -y)
    end
  elsif a.respond_to?(:nan?) and a.nan?
    a
  elsif a >= 0
    rsqrt(a)
  else
    Complex(0,rsqrt(-a))
  end
end