Euler Identity in Home

[Joe Horn]

(04-15-2014 09:17 PM)Manolo Sobrino Wrote:  Han, what's so hard to understand that if you claim to work with 12 significant digits, and you round in every step to 12 significant digits, and you store numbers with 12 significant digits, you can't simply give back results calculated with 25 significant digits? And adding insult to injury give them rounded to 12 in floating point?

You are assuming that we don't understand that. We DO understand it... and disagree with it. And for good reason, as the following hopefully makes clear.

If I want to calculate the sine of exactly 1 radian, then I would type sin(1), and of course I would intend it to mean sin(exactly 1.000000000000000000... radians). But YOU would say, "Oh no no no, that's wrong; sin(1) is using an input of only one significant digit, so the output should only have one significant digit, and any more digits than that in the output are bogus." At this point, you will of course object that you never said any such silly thing. Ah, but you have said it, over and over, every time you have insisted in this discussion that typing sin(3.14159265359) on an HP calculator cannot possibly be intended by the user to mean "give me the sine of exactly 3.141592653590000000000... radians". Apply that false assumption to sin(1) and you get the previously mentioned silly statement.

What's so hard to understand about this: HP allows the user to decide how many digits of the input are significant (including trailing zeros!), which then (as you mentioned!) requires the user to interpret the calculated result accordingly. When TI makes those decisions for the user, the user is prevented from exploring certain questions, such as "What is the sine of numbers very close to pi?" HP allows such exploration. Therefore HP can do what TI can't. Q.E.D.

Disclaimer: All of the above was my opinion when I wrote it, but I enjoy learning, and changing my opinions when that is warranted, so stay calm.