Reverse Polish Calculator

Implement a reverse polish notation calculator as described in class.

It must be interactive, the user types an expression and the result is
printed. That repeats until the user wants to stop. ctrl-D and ctrl-C
should both stop the calculator. Results must be given with at least
12 digits of accuracy, but no more than the precision of a double can
support.

Thorough error detection is required. If there is anything that is
(detectably) wrong with the formula or an improper calculation is
demanded (such as, but not limited to, division by zero) the user must
be told what is wrong, and no value for the expression may be displayed.
Errors must not cause the calculator to stop working.

The formulae consist of numbers (in the form of doubles), operators,
named functions, one named constant (pi), variables and assignments.
Do not attempt to do everything at once. Start simple, just numbers 
and a few operators at the beginning, and don't move forward until
everything is fully working. Save variables and assignemnt until last.

The parts of the expression will be space separated, numbers may be typed
in any way that would be accepted as a double constant in C++. That includes
optional + or -. Use strtod to convert from strings to doubles. The operators
must include + * - / and ^ (^ stands for to-the-power-of). Provide at least
20 functions including sqrt, sin, cos, log, and exp. There is no need to
create thos functions for yourself, you can use the <cmath> #include.

You must read a whole line of text from the user and extract the parts
from it with an istringstream. The end of the input line is the end of
the formula. #include <vector> to make the stack.

Variable names should consist only of letters, and must be insensitive to
case (radius, RADIUS, and raDiUs are the same variable). When a variable
name appears just treat it as a number, pushing its value onto the stack.
It is an error to use a variable that hasn't been given a value.

Assignment operations require a slight variation on the reverse polish
style: The symbol -> must always be followed by a variable name, and
represents setting that variable's value to whatever is currently on the
top of the stack.

For variables, you must create a special memory object (or struct or class)
which contains two equal-size vectors, one for names and one for values,
and methods for all the operations necessary. There aren't many.

Every feature must be properly tested, and your submissions must include
those tests, all from one continuous run of your program.

Example expressions                    and displayed results

  3 4 5 + *                              27

  3 4 5 + * -> radius                    27   (and now radius is 27)

  radius 2 ^ pi *                        2290.2210446696
  
  1 2 3 4 5 * * * * -> x 2 *             240  (and now x is 120)

  pi 0.25 * sin                          0.70710678118655

  2 4 5 1 - - / 3 +                      error - division by zero

  6.254175 3.745824 +                    9.999999

Your results do not have to exactly duplicate mine.
These examples are only examples, they do not constitute adequate testing.