Euler Identity in Home

[Manolo Sobrino]

(04-16-2014 03:09 PM)Han Wrote:  For Manolo -- just three simple questions:

1. When a user computes SIN(1.1) on any calculator (or Mathematica or Maple, etc), what should the calculator return? (Assume radian mode)

2. Same question, this time the user enters SIN(1.10) -- same value but with an extra significant digit. What should the returned result be? (Assume radian mode)

3. How should a real number be implemented so that a calculator can know the difference between 1.1 and 1.10 ?

1)&2)

In a world of perfect calculators I guess that you'll have to type 1.1 for 2 significant digits, 1.10 for three, 1.100 for four, and so on. That is, for instance if we're talking about 1.1*10^-10: 1.1E-10, 1.10E-10, 1.100E-10,... . Now in their default mode they assume that every number you type has 12 significant figures for the HP, 14 for the TI (those that I've discussed). That's OK if you understand what they're doing. BTW, they fill with zeroes and show you the rounded results to N when you work in FIX N mode.

And they should return, if not the multiple precision value according to that (people have no use for too low precision results, really), at least the most accurate value rounded to the significant digits of your input. They already do that in FIX mode.

About 3), I don't know. But the minimum should be that you implement a fixed number of significant digits, and using reasonable algorithms and round where it's due you get results for that number of significant digits, preferably no less, and it would be nice that no more, because it really makes no sense.