##
# = CMath
#
# CMath is a library that provides trigonometric and transcendental
# functions for complex numbers.
#
# == Usage
#
# To start using this library, simply:
#
#   require "cmath"
#
# Square root of a negative number is a complex number.
#
#   CMath.sqrt(-9)  #=> 0+3.0i
#

module CMath

  include Math

  alias exp! exp
  alias log! log
  alias log2! log2
  alias log10! log10
  alias sqrt! sqrt
  alias cbrt! cbrt

  alias sin! sin
  alias cos! cos
  alias tan! tan

  alias sinh! sinh
  alias cosh! cosh
  alias tanh! tanh

  alias asin! asin
  alias acos! acos
  alias atan! atan
  alias atan2! atan2

  alias asinh! asinh
  alias acosh! acosh
  alias atanh! atanh

  ##
  # Math::E raised to the +z+ power
  #
  #   exp(Complex(0,0))      #=> 1.0+0.0i
  #   exp(Complex(0,PI))     #=> -1.0+1.2246467991473532e-16i
  #   exp(Complex(0,PI/2.0)) #=> 6.123233995736766e-17+1.0i
  def exp(z)
    if z.real?
      exp!(z)
    else
      ere = exp!(z.real)
      Complex(ere * cos!(z.imag),
              ere * sin!(z.imag))
    end
  end

  ##
  # Returns the natural logarithm of Complex.  If a second argument is given,
  # it will be the base of logarithm.
  #
  #   log(Complex(0,0)) #=> -Infinity+0.0i
  def log(*args)
    z, b = args
    if z.real? and z >= 0 and (b.nil? or b >= 0)
      log!(*args)
    else
      a = Complex(log!(z.abs), z.arg)
      if b
        a /= log(b)
      end
      a
    end
  end

  ##
  # returns the base 2 logarithm of +z+
  def log2(z)
    if z.real? and z >= 0
      log2!(z)
    else
      log(z) / log!(2)
    end
  end

  ##
  # returns the base 10 logarithm of +z+
  def log10(z)
    if z.real? and z >= 0
      log10!(z)
    else
      log(z) / log!(10)
    end
  end

  ##
  # Returns the non-negative square root of Complex.
  #   sqrt(-1)            #=> 0+1.0i
  #   sqrt(Complex(-1,0)) #=> 0.0+1.0i
  #   sqrt(Complex(0,8))  #=> 2.0+2.0i
  def sqrt(z)
    if z.real?
      if z < 0
        Complex(0, sqrt!(-z))
      else
        sqrt!(z)
      end
    else
      if z.imag < 0 ||
        (z.imag == 0 && z.imag.to_s[0] == '-')
        sqrt(z.conjugate).conjugate
      else
        r = z.abs
        x = z.real
        Complex(sqrt!((r + x) / 2.0), sqrt!((r - x) / 2.0))
      end
    end
  end

  ##
  # returns the cube root of +z+
  def cbrt(z)
    if z.real?
      cbrt!(z)
    else
      Complex(z) ** (1.0/3)
    end
  end

  ##
  # returns the sine of +z+, where +z+ is given in radians
  def sin(z)
    if z.real?
      sin!(z)
    else
      Complex(sin!(z.real) * cosh!(z.imag),
              cos!(z.real) * sinh!(z.imag))
    end
  end

  ##
  # returns the cosine of +z+, where +z+ is given in radians
  def cos(z)
    if z.real?
      cos!(z)
    else
      Complex(cos!(z.real) * cosh!(z.imag),
              -sin!(z.real) * sinh!(z.imag))
    end
  end

  ##
  # returns the tangent of +z+, where +z+ is given in radians
  def tan(z)
    if z.real?
      tan!(z)
    else
      sin(z) / cos(z)
    end
  end

  ##
  # returns the hyperbolic sine of +z+, where +z+ is given in radians
  def sinh(z)
    if z.real?
      sinh!(z)
    else
      Complex(sinh!(z.real) * cos!(z.imag),
              cosh!(z.real) * sin!(z.imag))
    end
  end

  ##
  # returns the hyperbolic cosine of +z+, where +z+ is given in radians
  def cosh(z)
    if z.real?
      cosh!(z)
    else
      Complex(cosh!(z.real) * cos!(z.imag),
              sinh!(z.real) * sin!(z.imag))
    end
  end

  ##
  # returns the hyperbolic tangent of +z+, where +z+ is given in radians
  def tanh(z)
    if z.real?
      tanh!(z)
    else
      sinh(z) / cosh(z)
    end
  end

  ##
  # returns the arc sine of +z+
  def asin(z)
    if z.real? and z >= -1 and z <= 1
      asin!(z)
    else
      (-1.0).i * log(1.0.i * z + sqrt(1.0 - z * z))
    end
  end

  ##
  # returns the arc cosine of +z+
  def acos(z)
    if z.real? and z >= -1 and z <= 1
      acos!(z)
    else
      (-1.0).i * log(z + 1.0.i * sqrt(1.0 - z * z))
    end
  end

  ##
  # returns the arc tangent of +z+
  def atan(z)
    if z.real?
      atan!(z)
    else
      1.0.i * log((1.0.i + z) / (1.0.i - z)) / 2.0
    end
  end

  ##
  # returns the arc tangent of +y+ divided by +x+ using the signs of +y+ and
  # +x+ to determine the quadrant
  def atan2(y,x)
    if y.real? and x.real?
      atan2!(y,x)
    else
      (-1.0).i * log((x + 1.0.i * y) / sqrt(x * x + y * y))
    end
  end

  ##
  # returns the inverse hyperbolic sine of +z+
  def asinh(z)
    if z.real?
      asinh!(z)
    else
      log(z + sqrt(1.0 + z * z))
    end
  end

  ##
  # returns the inverse hyperbolic cosine of +z+
  def acosh(z)
    if z.real? and z >= 1
      acosh!(z)
    else
      log(z + sqrt(z * z - 1.0))
    end
  end

  ##
  # returns the inverse hyperbolic tangent of +z+
  def atanh(z)
    if z.real? and z >= -1 and z <= 1
      atanh!(z)
    else
      log((1.0 + z) / (1.0 - z)) / 2.0
    end
  end

  module_function :exp!
  module_function :exp
  module_function :log!
  module_function :log
  module_function :log2!
  module_function :log2
  module_function :log10!
  module_function :log10
  module_function :sqrt!
  module_function :sqrt
  module_function :cbrt!
  module_function :cbrt

  module_function :sin!
  module_function :sin
  module_function :cos!
  module_function :cos
  module_function :tan!
  module_function :tan

  module_function :sinh!
  module_function :sinh
  module_function :cosh!
  module_function :cosh
  module_function :tanh!
  module_function :tanh

  module_function :asin!
  module_function :asin
  module_function :acos!
  module_function :acos
  module_function :atan!
  module_function :atan
  module_function :atan2!
  module_function :atan2

  module_function :asinh!
  module_function :asinh
  module_function :acosh!
  module_function :acosh
  module_function :atanh!
  module_function :atanh

  module_function :frexp
  module_function :ldexp
  module_function :hypot
  module_function :erf
  module_function :erfc
  module_function :gamma
  module_function :lgamma

end