--[[ Square Root by Newton's Method
     Functional Programming Example
     H. Conrad Cunningham, Professor
     Computer and Information Science
     University of Mississippi

Developed for CSci 658, Software Language Engineering, Fall 2013

1234567890123456789012345678901234567890123456789012345678901234567890

2013-09-08: Completed prototype

This square root function is adapted from section 1.1.7 of Abelson and
Sussman's Structure and Interpretation of Computer Programs (SICP)
textbook.

--]]

-- Function "sqrt" computes the square root of its argument "x" using
-- Newton's method.

local function sqrt(x)

  local function square(x)
    return x * x
  end

  local function good_enough(guess,x)
    return math.abs(square(guess)- x) < 0.001
  end

  local function average(x,y)
    return (x + y) / 2
  end

  local function improve(guess,x)
    return average(guess,x/guess)
  end

  local function sqrt_iter(guess,x)
    if good_enough(guess,x) then
      return guess
    else
      return sqrt_iter(improve(guess,x),x)
    end
  end

  if type(x) == "number" and x >= 0 then
    return sqrt_iter(1,x)
  else
    error("Square root cannot be computed for " .. tostring(x), 2)
  end
end


-- Testing of sqrt

local testvals = {0,1,2,3,4,5,6,7,8,9,10,16,25,36,
                  49,64,81,99,100,1000,10000}

print("\nSquare Root")
for _, v in ipairs(testvals) do
  print("sqrt(" .. tostring(v) .. ") = " .. tostring(sqrt(v)))
end