I am playing with a newly acquired HP-48G as I write this and it keeps me amazed. Other machines may have gimmicks like a color display, but in terms of functionality, the HP-48 series is far superior to anything I've ever seen. Just as keystroke programmable calculators were a perfect learning tool for the programmer of the 70s or the early 80s, this machine with its object-oriented User RPL language is the perfect learning tool for the 90s and beyond. But it's more than just a learning tool: all HP-48 calculators are serious professional instruments.

To demonstrate this, I decided to do something different. For the majority of calculators shown on this Web site (with the exception of a few very low-end machines that don't support this) the programming example I present is an implementation of the Gamma function. For the HP-28/48 series of calculators, I have already presented a complex implementation of this function, and an implementation of the incomplete Gamma function as well. There are only so many variations on a theme!

Fortunately, just a few days ago I was able to assist someone on the Internet with an HP-48 programming question, and it gave me the opportunity to practice my RPL programming skills. The question was this: how do you create a program that calculates the radius of curvature? For any function f(x), the radius of curvature at any x=x₀ can be obtained by evaluating (1+(f'(x)²))^3/2/f''(x). So, can we create a program that takes a number (x₀) and a function as arguments on the stack, and returns a number that's the value of the radius of curvature we seek?

Few programming languages offer such a powerful feature (in fact, the only non-HP machines that I know about that are capable of this feat are the TI-89 and TI-92). Were we to use C++, we would be forced to write a sophisticated expression evaluator (or alternatively, we would have to resort to using a third party library.) Not so with User RPL, as the program below neatly demonstrates.

To use this program, enter an expression using an independent variable, the name of the independent variable, a value. For instance, enter the following arguments:

'X^3'
'X'
2

When you invoke the program (I stored it under the name ROC on my calculator) within a couple of seconds, the display will show the result: 145.50260116. You can also use ROC in algebraic expressions (e.g., 'ROC(X^3,X,2)'). Please note that using this program requires that your calculator be placed in symbolic mode (-3 CF). For this reason, you cannot use ->NUM on expressions containing ROC, nor can you use ROC as a plot function without writing a suitable wrapper function.

«
  -> fX x x0
  «
    fX x ∂ DUP -> dfX
    «
      dfX x ∂
    »
    SWAP 2 ^ 1 + 3 ^ √ SWAP / -> fR
    «
      fR x x0 2 ->LIST |
    »
  »
»