### arctan =====================================================================

Tags
----
scripting, JS, internal, treenode, general concept

Parameters
----------
x

General description
-------------------
Returns the inverse tangent of x.

###

Eval_arctan = ->
  push(cadr(p1))
  Eval()
  arctan()

arctan = ->
  d = 0

  save()

  p1 = pop()

  if (car(p1) == symbol(TAN))
    push(cadr(p1))
    restore()
    return

  if (isdouble(p1))
    errno = 0
    d = Math.atan(p1.d)
    if (errno)
      stop("arctan function error")
    push_double(d)
    restore()
    return

  if (isZeroAtomOrTensor(p1))
    push(zero)
    restore()
    return

  if (isnegative(p1))
    push(p1)
    negate()
    arctan()
    negate()
    restore()
    return

  # arctan(sin(a) / cos(a)) ?

  if (Find(p1, symbol(SIN)) && Find(p1, symbol(COS)))
    push(p1)
    numerator()
    p2 = pop()
    push(p1)
    denominator()
    p3 = pop()
    if (car(p2) == symbol(SIN) && car(p3) == symbol(COS) && equal(cadr(p2), cadr(p3)))
      push(cadr(p2))
      restore()
      return

  # arctan(1/sqrt(3)) -> pi/6
  # second if catches the other way of saying it, sqrt(3)/3

  if (car(p1) == symbol(POWER) && equaln(cadr(p1), 3) && equalq(caddr(p1), -1, 2)) or
  (car(p1) == symbol(MULTIPLY) && equalq(car(cdr(p1)), 1,3) and car(car(cdr(cdr(p1)))) == symbol(POWER) && equaln(car(cdr(car(cdr(cdr(p1))))),3) && equalq(car(cdr(cdr(car(cdr(cdr(p1)))))), 1, 2))
    push_rational(1, 6)
    if evaluatingAsFloats
      push_double(Math.PI)
    else
      push(symbol(PI))
    multiply()
    restore()
    return

  # arctan(1) -> pi/4

  if (equaln(p1, 1))
    push_rational(1, 4)
    if evaluatingAsFloats
      push_double(Math.PI)
    else
      push(symbol(PI))
    multiply()
    restore()
    return

  # arctan(sqrt(3)) -> pi/3

  if (car(p1) == symbol(POWER) && equaln(cadr(p1), 3) && equalq(caddr(p1), 1, 2))
    push_rational(1, 3)
    if evaluatingAsFloats
      push_double(Math.PI)
    else
      push(symbol(PI))
    multiply()
    restore()
    return

  push_symbol(ARCTAN)
  push(p1)
  list(2)

  restore()