..  _lab5-cube-root:

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Lab 5 - Calculating the cube root
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By now, you should have some experience setting up a simple program.
Let's try another problem similar to our first homework problem. Instead
of working on the square root problem, let's see if we can figure out
the cube root. This time, we will let a mathematician tell us how to do
this! 

*********************
The Problem statement
*********************

If ``X`` is the number we want the cube root of, and ``A`` is our guess, then
``X`` should equal ``A*A*A``.

The scheme we will use
======================

Here is what Isaac Newton has to say on the matter:

Start off with some guess for A. (You might try something simple like X/2 as a
start.)  Calculate each new guess using this formula:

..  code-block:: text

    A = 1/3 *( X/(A*A) + 2 * A)


..  note::

    You might wonder why all those parentheses are in there. I want to make
    sure we ask the computer to evaluate the right formula. 

The line above is an "assignment statement". The variable "A" appears on both
sides of the equal sign. On the right side, the value for "A" is the previous
guess. We evaluate the formula to produce a new guess, and save this new guess
in the variable "A" for the next pass through the loop.  You stop when the
difference between the previous guess and the next guess is small enough to
suit you.

***************
Your assignment
***************

Using the basic flow of the lab4 as a guide, and the example we worked in
class, create a new C++ program in a file called ``cuberoot.cpp``. Your program
should prompt the user for an input number. It should then use the scheme shown
above to generate an initial guess for the cube root of that number. It should
then loop generating a new guess until the guess is accurate enough to suite
you. (You get to pick the accuracy, but it should be better than a few digits
past the decimal point. Think about how accurate your calculator is and see if
you can do at least that well.

You can read a number from the user using this:

..  code-block:: text

    double  mynum;

    ...

    cin >> mynum;

This example reads in a real number (with a decimal point in it). The angle
brackets go toward the variable that will receive the input. The user enters a
number, then presses the "return" (or "enter") key.

As you test your program, print out each guess using a line like this"

..  code-block::    text

    Current guess for the cube root is x.xxxxxx, this is off by x.xxxxx

You should see a number of these lines until you decide the accuracy is good enough.

Now, run the program on a number of values you pick. Make sure you see how well
you are doing. Your final output should give the final answer to the user. You
decide how to display that.

..  note::

    There are hints on how to approach this problem in :ref:`cosc1315-lab5-hints`

***************
What to turn in
***************

Submit your ``cuberoot.cpp`` program source file on Blackboard in the Lab6 Lab
area.