Module: Math

Defined in:
lib/mathn.rb

Instance Method Summary collapse

Instance Method Details

#rsqrt(a) ⇒ Object 



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# File 'lib/mathn.rb', line 256

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/mathn.rb', line 233

def sqrt(a)
  if a.kind_of?(Complex)
    abs = sqrt(a.real*a.real + a.image*a.image)
#      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.image >= 0 
	Complex(x, y)
    else
	Complex(x, -y)
    end
  elsif a >= 0
    rsqrt(a)
  else
    Complex(0,rsqrt(-a))
  end
end