Math

 
               # File complex.rb, line 562
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 594
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 570
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 602
def asinh(z)
  if Complex.generic?(z)
    asinh!(z)
  else
    log( z + sqrt(1.0+z*z) )
  end
end
            

 
               # File complex.rb, line 578
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 586
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 610
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 491
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 527
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 482
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 544
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 554
def log10(z)
  if Complex.generic?(z)
    log10!(z)
  else
    log(z)/log!(10)
  end
end
            

 
               # File complex.rb, line 501
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 519
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 463
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 511
def tan(z)
  if Complex.generic?(z)
    tan!(z)
  else
    sin(z)/cos(z)
  end
end
            

 
               # File complex.rb, line 535
def tanh(z)
  if Complex.generic?(z)
    tanh!(z)
  else
    sinh(z)/cosh(z)
  end
end