### arcsin =====================================================================

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

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

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

###

Eval_arcsin = ->
  push(cadr(p1))
  Eval()
  arcsin()

arcsin = ->
  n = 0
  d = 0

  save()

  p1 = pop()

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

  if (isdouble(p1))
    errno = 0
    d = Math.asin(p1.d)
    if (errno)
      stop("arcsin function argument is not in the interval [-1,1]")
    push_double(d)
    restore()
    return

  # if p1 == 1/sqrt(2) then return 1/4*pi (45 degrees)
  # second if catches the other way of saying it, sqrt(2)/2

  if (isoneoversqrttwo(p1)) or
  (car(p1) == symbol(MULTIPLY) && equalq(car(cdr(p1)), 1,2) and car(car(cdr(cdr(p1)))) == symbol(POWER) && equaln(car(cdr(car(cdr(cdr(p1))))),2) && equalq(car(cdr(cdr(car(cdr(cdr(p1)))))), 1, 2))
    push_rational(1, 4)
    push_symbol(PI)
    multiply()
    restore()
    return

  # if p1 == -1/sqrt(2) then return -1/4*pi (-45 degrees)
  # second if catches the other way of saying it, -sqrt(2)/2

  if (isminusoneoversqrttwo(p1)) or
  (car(p1) == symbol(MULTIPLY) && equalq(car(cdr(p1)), -1,2) and car(car(cdr(cdr(p1)))) == symbol(POWER) && equaln(car(cdr(car(cdr(cdr(p1))))),2) && equalq(car(cdr(cdr(car(cdr(cdr(p1)))))), 1, 2))
    if evaluatingAsFloats
      push_double(-Math.PI / 4.0)
    else
      push_rational(-1, 4)
      push_symbol(PI)
      multiply()
    restore()
    return

  # if p1 == sqrt(3)/2 then return 1/3*pi (60 degrees)
  if (issqrtthreeovertwo(p1))
    if evaluatingAsFloats
      push_double(Math.PI / 3.0)
    else
      push_rational(1, 3)
      push_symbol(PI)
      multiply()
    restore()
    return

  # if p1 == -sqrt(3)/2 then return -1/3*pi (-60 degrees)
  if (isminussqrtthreeovertwo(p1))
    if evaluatingAsFloats
      push_double(-Math.PI / 3.0)
    else
      push_rational(-1, 3)
      push_symbol(PI)
      multiply()
    restore()
    return

  if (!isrational(p1))
    push_symbol(ARCSIN)
    push(p1)
    list(2)
    restore()
    return

  push(p1)
  push_integer(2)
  multiply()
  n = pop_integer()

  switch (n)

    when -2
      if evaluatingAsFloats
        push_double(-Math.PI / 2.0)
      else
        push_rational(-1, 2)
        push_symbol(PI)
        multiply()

    when -1
      if evaluatingAsFloats
        push_double(-Math.PI / 6.0)
      else
        push_rational(-1, 6)
        push_symbol(PI)
        multiply()

    when 0
      if evaluatingAsFloats
        push_double(0.0)
      else
        push(zero)

    when 1
      if evaluatingAsFloats
        push_double(Math.PI / 6.0)
      else
        push_rational(1, 6)
        push_symbol(PI)
        multiply()

    when 2
      if evaluatingAsFloats
        push_double(Math.PI / 2.0)
      else
        push_rational(1, 2)
        push_symbol(PI)
        multiply()

    else
      push_symbol(ARCSIN)
      push(p1)
      list(2)

  restore()