# Tangent function of numerical and symbolic arguments



Eval_tan = ->
  push(cadr(p1))
  Eval()
  tangent()

tangent = ->
  save()
  yytangent()
  restore()

yytangent = ->
  n = 0
  d = 0.0

  p1 = pop()

  if (car(p1) == symbol(ARCTAN))
    push(cadr(p1))
    return

  if (isdouble(p1))
    d = Math.tan(p1.d)
    if (Math.abs(d) < 1e-10)
      d = 0.0
    push_double(d)
    return

  # tan function is antisymmetric, tan(-x) = -tan(x)

  if (isnegative(p1))
    push(p1)
    negate()
    tangent()
    negate()
    return

  # multiply by 180/pi to go from radians to degrees.
  # we go from radians to degrees because it's much
  # easier to calculate symbolic results of most (not all) "classic"
  # angles (e.g. 30,45,60...) if we calculate the degrees
  # and the we do a switch on that.
  # Alternatively, we could look at the fraction of pi
  # (e.g. 60 degrees is 1/3 pi) but that's more
  # convoluted as we'd need to look at both numerator and
  # denominator.

  push(p1)
  push_integer(180)
  multiply()
  if evaluatingAsFloats
    push_double(Math.PI)
  else
    push_symbol(PI)
  divide()

  n = pop_integer()

  # most "good" (i.e. compact) trigonometric results
  # happen for a round number of degrees. There are some exceptions
  # though, e.g. 22.5 degrees, which we don't capture here.
  if (n < 0 || isNaN(n))
    push(symbol(TAN))
    push(p1)
    list(2)
    return

  switch (n % 360)
    when 0, 180
      push_integer(0)
    when 30, 210
      push_rational(1, 3)
      push_integer(3)
      push_rational(1, 2)
      power()
      multiply()
    when 150, 330
      push_rational(-1, 3)
      push_integer(3)
      push_rational(1, 2)
      power()
      multiply()
    when 45, 225
      push_integer(1)
    when 135, 315
      push_integer(-1)
    when 60, 240
      push_integer(3)
      push_rational(1, 2)
      power()
    when 120, 300
      push_integer(3)
      push_rational(1, 2)
      power()
      negate()
    else
      push(symbol(TAN))
      push(p1)
      list(2)