# File complex.rb, line 534
  def acos(z)
    if Complex.generic?(z) and z >= -1 and z <= 1
      acos!(z)
    else
      -1.0.im * log( z + 1.0.im * sqrt(1.0-z*z) )
    end
  end

# File complex.rb, line 566
  def acosh(z)
    if Complex.generic?(z) and z >= 1
      acosh!(z)
    else
      log( z + sqrt(z*z-1.0) )
    end
  end

# File complex.rb, line 542
  def asin(z)
    if Complex.generic?(z) and z >= -1 and z <= 1
      asin!(z)
    else
      -1.0.im * log( 1.0.im * z + sqrt(1.0-z*z) )
    end
  end

# File complex.rb, line 574
  def asinh(z)
    if Complex.generic?(z)
      asinh!(z)
    else
      log( z + sqrt(1.0+z*z) )
    end
  end

# File complex.rb, line 550
  def atan(z)
    if Complex.generic?(z)
      atan!(z)
    else
      1.0.im * log( (1.0.im+z) / (1.0.im-z) ) / 2.0
    end
  end

# File complex.rb, line 558
  def atan2(y,x)
    if Complex.generic?(y) and Complex.generic?(x)
      atan2!(y,x)
    else
      -1.0.im * log( (x+1.0.im*y) / sqrt(x*x+y*y) )
    end
  end

# File complex.rb, line 582
  def atanh(z)
    if Complex.generic?(z) and z >= -1 and z <= 1
      atanh!(z)
    else
      log( (1.0+z) / (1.0-z) ) / 2.0
    end
  end

# File complex.rb, line 463
  def cos(z)
    if Complex.generic?(z)
      cos!(z)
    else
      Complex(cos!(z.real)*cosh!(z.image),
              -sin!(z.real)*sinh!(z.image))
    end
  end

# File complex.rb, line 499
  def cosh(z)
    if Complex.generic?(z)
      cosh!(z)
    else
      Complex( cosh!(z.real)*cos!(z.image), sinh!(z.real)*sin!(z.image) )
    end
  end

# File complex.rb, line 454
  def exp(z)
    if Complex.generic?(z)
      exp!(z)
    else
      Complex(exp!(z.real) * cos!(z.image), exp!(z.real) * sin!(z.image))
    end
  end

# File complex.rb, line 516
  def log(z)
    if Complex.generic?(z) and z >= 0
      log!(z)
    else
      r, theta = z.polar
      Complex(log!(r.abs), theta)
    end
  end

# File complex.rb, line 526
  def log10(z)
    if Complex.generic?(z)
      log10!(z)
    else
      log(z)/log!(10)
    end
  end

# File complex.rb, line 473
  def sin(z)
    if Complex.generic?(z)
      sin!(z)
    else
      Complex(sin!(z.real)*cosh!(z.image),
              cos!(z.real)*sinh!(z.image))
    end
  end

# File complex.rb, line 491
  def sinh(z)
    if Complex.generic?(z)
      sinh!(z)
    else
      Complex( sinh!(z.real)*cos!(z.image), cosh!(z.real)*sin!(z.image) )
    end
  end

# File complex.rb, line 435
  def sqrt(z)
    if Complex.generic?(z)
      if z >= 0
        sqrt!(z)
      else
        Complex(0,sqrt!(-z))
      end
    else
      if z.image < 0
        sqrt(z.conjugate).conjugate
      else
        r = z.abs
        x = z.real
        Complex( sqrt!((r+x)/2), sqrt!((r-x)/2) )
      end
    end
  end

# File complex.rb, line 483
  def tan(z)
    if Complex.generic?(z)
      tan!(z)
    else
      sin(z)/cos(z)
    end
  end

# File complex.rb, line 507
  def tanh(z)
    if Complex.generic?(z)
      tanh!(z)
    else
      sinh(z)/cosh(z)
    end
  end