Skip to content(if available)orjump to list(if available)

Personal calculator has key to solve any equation f(x)=0 (1979) [pdf]


Check out the author. For those not in the know, Kahan was the driving architect behind IEEE 754 -- pretty much the basis of all computer floating point now. See

I remember seminars at Berkeley where equipment manufactures show up to talk about their gear and Kahan would sit in the front row and grill them over their floating point implementations.


So that is where Kahan summation algorthm comes from!


I had one of these way back when, and loved it.

This is a great article, and reading it might give younger folks an idea of why HP users from the 1900s loved their calculators so much. They were designed for people who needed to get things done. And it wasn't just the algorithms inside. The physical machines were terrific, too. The pivoting keys left no doubt as to whether you had entered a digit (or whether, as in competitors' machines, the keystroke had entered the digit twice by mistake). And then there's RPN. Oh, lovely RPN -- trusty friend to those who needed correct answers and needed them in a rush.

Such elegance (of machines and writing) is rare nowadays.

Thanks for posting this, which brought back good memories.


A friend introduced me to the HP-40G in high school, while everybody was using TI or Casio. Turns out these calculators can beep with a given frequency! So I learned (some of) the physics of sound to be able to program music. So it really pushed me to do more advanced maths and taught me programming, these are some fondly remembered days.

The symbolic computation GUI is also a marvel of design that is unsurpassed to this day, especially in how you can select semantic blocks with a keyboard, and how good the rendering is. It felt like a human-centric interface rather than a computer-centric one. Although the general UI of the calculator was more of a confusing mess, so it had its flaws.

Well, I got mine for cheap from another student who "bought this useless garbage" so it's not a universal point of view.


My HP 48 was a life saver from high school through college. Everything you said nailed it. I can still feel the press of those keys.

Whenever I had to borrow or do something on a friends TI, I couldn’t stand it. The wobbly keys made typing all those parentheses even more of a nightmare!


Keys set aside, one can now use Free42 on a phone to get a taste.


People from 2020 still love the too, ha ha. I have several 35s at work and just got a Swiss Micros DM42 from xmas. Then again, I'm 50 and used these all through EE school and my profession. I have four 32sii still sealed in clamshell package. Went out and bought a bunch years ago when they discontinued them.


One of my biggest regrets was passing up an offer to buy over 200 HP48 calculators back in the early 2000s. There was an independent book store across the street from a local tech school that had bought used 48s from students. There was one professor who required them for her class but she left and they could not move their inventory. They did have some black screen 48GX so I got those, but I should have picked up the whole lot.


They seem to be going for about $300 used, though considering inflation less than new. If you could have gotten a good deal, then you’d come out ahead. The price will only increase. I have a 48G and 48GX, and several others. I’d like to collect them all and build a nice display case to house them.


I had an HP48SX in high school, then upgraded to a 48G. I remember programming games on it.


i am in high school and the 48GX is undeniably the best calculator that i've ever had to use. unfortunately i don't have the serial cable for it so i can't load anything cool like metakernel i wish there was a modern alternative with the same simplicity :(


There's a very long interview with Kahan on ACM's YouTube channel. Here's a link to the part where he talks about the "Solve" button:


When you watch Sussman and Steele give the MIT 6001 course the audience are seasoned HP calculator guys and gals

These must be the team who were designing the HP-28S and user rpl - the beautiful love child of Forth and Lisp.

And what a calculator they put out!


RPL is just magic. It's really fun to work with.

It's hard to appreciate what you're holding in your hand when you have one of these machines. When I learned the 48s had both Kermit and a serial port, the clouds parted and the sun came out. Really extraordinary capability in a $99 calculator.

Always liked the form factor of the 28s, just needed a way to get code on and off (besides the printer port) of them.


And a better battery port. Also, dont confuse A23 batteries for N.

But ya, i always like the 28 more than the 48.

Have you heard of RPL/2? A modern implementation of RPL meant for scientific computing? Its annoying to compile but its quite nice!


Admittedly it's kind of late for 1979, but I feel like this can be done better using exact differentiation. You don't need to take the symbolic derivative; just use the dual numbers to evaluate the derivative at a single point. Then the secant method becomes Newton's method.

Also, assuming that a second guess isn't provided, how does the calculator choose one? I'd imagine there are numerical precision problems that make choosing one hard.


Wait, is it using this algorithm? "False position": . I thought it was using something primitive like the "secant method": . But the article suggests that it tries to be more clever than that.




I used this to get the optimum fuel burn for the moon lander game on the hp67.

From memory it was a single 45 unit burn (about half the fuel) in the final moment.


Yes, suicide burns tend to be most efficient.


Yeah the deceleration would have squashed the astronauts but the landing velocity was zero. So a win.


I didn't realize at the time how much I learned from my HP-15c manual, which had a similar treatment of its numerical algorithms. Thanks HP!


Some years ago I bought a printing desk calculator. The manufacturer apparently wanted to minimize their translation bill for the manual, so it almost completely avoided any textual explanation, instead illustrating how to use all of the functions by showing number lines with arrows and the corresponding calculator buttons. At first it was frustrating but after getting used to it I actually thought it was pretty neat, as it encouraged a more intuitive understanding of exactly what the calculator buttons did.

Relatedly I learned a whole lot of algebra from reading a slide rule manual. I don't think I had a good intuitive understanding of logarithms until I saw them as pictures with arrows showing how they work on the slide rule. And then the manual was full of practical ways to reduce various common math problems to problems that are easy to solve with the slide rule, usually by figuring out how to express them as powers or logarithms.


I'm really interested in reading these manuals. Do you recall what were they for?


For the former I unfortunately cannot find a copy and I don't have the calculator any more... my hazy recollection is that it was a Panasonic printing desk calculator I bought at Staples but that could be wrong. Fwiw the newer desk calculators seem to all have pretty bad keypads so if you want a calculator that's really comfortable to use for fast totaling you might want to get a "vintage" one from when they were using mechanical key switches. Part of the reason I got rid of the one I had is because I was having issues with it not always registering keypresses when I thought it would have.

As for the slide rule, I believe it was a Pickett booklet, likely one of the ones that have fortunately been archived here:

The Asimov slide rule book is also very good and I have a copy. I believe I inherited it, along with several slide rules, from my grandfather who had been an EE at the NIST and also fastidiously kept a lot of things he had bought for grad school. One of the slide rules has "US Government Property" silkscreened on with the scales which is fairly neat, I assume DoD or someone had had a large number made on contract like they used to do with office supplies. I also have a US Government Property set of drafting tools that I use when hand-drafting sewing patterns.


I had a similar experience with slide rule books I checked out from the public library in the 1970s. Looking on Amazon now, I see 'An Easy Introduction to the Slide Rule' by none other than Issac Asimov. It's entirely possible that this is the book I used, and I think it might fit your bill.


I use a DM-42 nearly every day. A German company (Moravia) has recently taken over HP’s calculator operations which gives me hope.


Oh, that picture brings back memories...


If this were true it could also solve the halting problem on Turing machines with bounded memory. At least if x is vector valued.