###
 Convert complex z to clock form

  Input:    push  z

  Output:    Result on stack

  clock(z) = abs(z) * (-1) ^ (arg(z) / pi)

  For example, clock(exp(i pi/3)) gives the result (-1)^(1/3)
###

# P.S. I couldn't find independent definition/aknowledgment
# of the naming "clock form" anywhere on the web, seems like a
# naming specific to eigenmath.
# Clock form is another way to express a complex number, and
# it has three advantages
#   1) it's uniform with how for example
#      i is expressed i.e. (-1)^(1/2)
#   2) it's very compact
#   3) it's a straighforward notation for roots of 1 and -1


DEBUG_CLOCKFORM = false

Eval_clock = ->
  push(cadr(p1))
  Eval()
  clockform()

clockform = ->
  save()
  #if 1
  p1 = pop()
  push(p1)
  abs()
  if DEBUG_CLOCKFORM then console.log "clockform: abs of " + p1 + " : " + stack[tos-1]

  # pushing the expression (-1)^... but note
  # that we can't use "power", as "power" evaluates
  # clock forms into rectangular form (see "-1 ^ rational"
  # section in power)
  push_symbol(POWER)

  push_integer(-1)

  push(p1)
  arg()
  if DEBUG_CLOCKFORM then console.log "clockform: arg of " + p1 + " : " + stack[tos-1]
  if evaluatingAsFloats
    push_double(Math.PI)
  else
    push(symbol(PI))
  divide()
  if DEBUG_CLOCKFORM then console.log "clockform: divide : " + stack[tos-1]
  list(3)

  if DEBUG_CLOCKFORM then console.log "clockform: power : " + stack[tos-1]
  multiply()
  if DEBUG_CLOCKFORM then console.log "clockform: multiply : " + stack[tos-1]
  #else
  ###
  p1 = pop()
  push(p1)
  abs()
  push(symbol(E))
  push(p1)
  arg()
  push(imaginaryunit)
  multiply()
  power()
  multiply()
  ###
  #endif
  restore()