Kahan on HP calculators: Solve, Integrate and Matrix Operations

i think my work with hp which continued when they moved the calculator division from cupertino up to corvallis oregon um that work was very fruitful i enjoyed the people with whom i was working when i went up there one day they were having a picnic outside they have a spacious lawn there it was lovely green beautiful day and i thought i'd bother the project manager stan mintz and i wanted to get a solved key on the calculator i wanted to arrange that if it's a programmable calculator and you can program the left-hand side of an equation that then i'd like the calculator to search for the root and i had an algorithm for doing it which i thought would converge at adequate speed and a way of deciding when to quit and so on and that's what i wanted to put into a calculator and uh stan had resisted me because he'd said i've asked this the marketing people and they say no one has ever asked for a solved key of course they wouldn't ask for salty he wouldn't have dawned on them perhaps that they could have it but finally we were at this picnic and stan spiked the punch which is very much contrary to hp rules i'm t total so it didn't affect me but saying stan got zolly and he said i tell you what principal i'll let you have your solve key if you can provide me with an integrate key i was never able to integrate when i went to college give me an integrate key and you can have the solve k2 well how could i resist that challenge so i did come up with an integrate key that would fit in the space that the space available was very small just a handful of registers were available for scratch and dennis harms helped me work on it and microcode it and so we got it working and then the solve key and they got put into the hp 34c and i have one but its battery is dead so i'm not going to bring it out well the thing was though that the hp 34c's solve key and integrate keys were now interesting challenges since things could go wrong some equations don't have solutions some equations give you the wrong solution because when you compute the left-hand side of the equation the round off gives you junk and integrals can be even more interesting so i wanted the guys who write the manuals to include this kind of information in the manual so it helped people use these very powerful keys correctly uh but hp had a policy and the policy was we don't put tutorial material in our manuals because we're dealing with professionals like us we know what we're doing they know what they're doing and besides professor khan are you telling us that you've persuaded us to put something in a calculator that can get wrong answers well um i seduced the marketing guys and they put in an extra chapter in the hp 34c manual and then the their manager said hey i told you not to put that in take it out and they said well if we take it out we're going to delay the completion of the manual that'll delay that getting the captain on the market so there he was blackmailed in effect he had to leave the stuff in and they won a prize at the willamette valley technical writers association for technical manuals partly because of these chapters and when the sales people did surveys they found that several of their customers said i bought the calculator because those chapters tell me how to use it and and i can use it more easily than i can on mainframes so we were vindicated um in the meantime the financial calculators were getting uh complicated and that's because of something called internal rate of return um i've got one of the financial calculators here yes has an irr key now internal rate of return is a fictional interest rate but explains what what rate of interest are we making on our investment and that is the internal rate return and requires that you solve an equation which can be fairly complicated in fact under some circumstances you could have a polynomial of degree in the tens of thousands to solve but the calculator only does so many arithmetic operations per second the slow ones are seven half arithmetic operations per second and you'd really like to get the answer in 20 or 30 seconds because most people won't wait any longer that was a challenge and i found a way to do it now we had a calculator financial account not only was it accurate the air is confined to when you're in the last digit displayed not only is it accurate but it solves the internal rate of return problem and it solves these problems including some for mortgages and and and uh kinds of investments uh discounts it solves them accurately and quickly whereas on the then competing texas instance instruments business analyst you could put in the data and the calculator was supposed to solve the problem but it would go catatonic or it would run run run run run run never stop or it would give you a junk answer that wouldn't happen on my program yes and as i recall i thought i'd proved it so we really had a superior beast well the success of that calculator made my next demand sound more credible i wanted a calculator that had not just the solve and integrate keys i wanted to have complex variables and small matrices so that it would have everything for sophomore engineering students exceptive scrads and curls gives grads and curls require a larger display and i got them to build it and that was that was this one here that's the 15c uh it really is my favorite now in order to get them to build it i had to make an estimate of the market so what i did was go to our library here and i looked up all the colleges i could think of that had engineering schools and i looked at their enrollments and i figured that about half of the incoming class each year would want to buy this calculator why have because when i used the hp 34c the one would just solve and integrate i would plant myself in the library or i plant myself out in sproul plaza at a table and i pretend to be working with this calculator students would come up and ask what i was doing and if they're engineering students they'd say oh and what does that do and i'd show them and half of them would go to the student bookstore just on the other side of the plaza and buy one with their own money yes not waiting for a doting ant or something like that to buy one for them so i figured half the students are going to buy one

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Length: 8min 26sec (506 seconds)

Published: Sun Nov 15 2020