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What is old is new: RPN on the HP 35s Scientific Calculator

I saw the 35s for the first time in a Staples store just this year, though the calculator has been around in University bookstores since 2007. I bought mine on sale, being listed at $99.00 full price. When it came out in 2007, I heard that it came with a zippered pouch to store the calculator in. Mine, supposedly the 2011 model, came with a vinyl pouch that was open, with rather stiff elasticized cloth bands on the sides, making the calculator difficult to actually place in its pouch, especially the first time it was used.  Once in the pouch, it was difficult to take back out of its pouch. The calculator feels light when held in one’s hand. I’m not sure why I noticed that. Somehow I thought it would feel more substantial, given all of the functions and programmability, and the 800 or so memories that it boasts of.

2012 will be the 40th anniversary of the scientific calculator. HP made the world’s first scientific calculator in 1972, and it was an RPN calculator with no algebraic mode. Anyone who has tried to program in a serious way would appreciate that RPN is easier to program for (from the manufacturer’s point of view), because of its reliance on a memory model called “stacks”, which most computer science undergraduates know about, by second year at the latest. While the act of doing things algebraically might seem easier to us humans, programming a calculator to think in terms of human algebra is more difficult than you would think. It takes a computer many more steps, and thus it is much slower than RPN in terms of processor time. It was probably not until the early 1990s that calculators were capable of anything close to human-style algebra, and only recently have processors become so small and fast that the speed of the algorithm is not really as important as it used to be. But human speed might be. To those who take the time to understand how RPN works, and how the 35s implements stacks, RPN is still faster for humans to perform calculations.

Many of the features on the 35s are common on much cheaper calculators: statistics, regression, vectors, mixed fractions, complex numbers, numberical integration, numerical differentiation, a linear solver, and there are much cheaper calculators that can solve single-variable polynomials up to order 3. I own a $5.00 calculator that can solve linear systems in up to 3 unknowns. Also, there are too many features on the “new” HP 35s that are tied up in menus, which is something that turned me off from using TI calculators. The only tangible attraction I can think of for this calculator is likely to be its programming mode. The 35s is among the very few non-graphical calculators around today that one can write programs in.

Playing with it a bit, I find that scientific notation seems to work up to 10500, meaning the computation of factorials can go to unheard-of extremes, even going beyond the capacity of an Excel spreadsheet. I was able to find, to several sig figs, the value of 253!, wheras Excel 2007 craps out past 125!. This means that this calculator is particularly powerful for performing permutations (nPr) and combinations (nCr).

I have lost my touch with the use of stacks from my programming days, but it looks like the calculator does a lot of pushing and popping, even in the middle of the stack. In addition, it only seems to perform calculations on the stack 2 at a time, even though the stack can accomodate 4 numbers. When you enter numbers, it’s like “pushing” numbers on to the bottom of the stack. You enter a number, and the stack moves up. If  you enter two numbers then add them, the stack moves down and the result of the addition is entered in the immediate register in the stack, called “x”.  The true implemtnation of this is that, for the registers t, z, y, and x, t gets its number copied to z, z copies to y, and y copies to x. This results in a duplication of t in the stack. If a “+” is pressed when a stack contains the numbers “1 2 3 4”, it adds only 3 and4, then the top 2 registers shift down and the result of adding 3 and 4 is placed in “x”: “1 1 2 7” becomes the resulting stack. The “1” and “2” shift down, but in reality, the memopry register values are just copied.

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