I'm the author of Scalar (http://scalarapp.com), another calculator replacement for iPhone / iPad. Just tested both versions of Tydlig very heavily, looks like the author ran into lots of the similar math/UI problems as I did when I was working on my app. :) Some approaches he has chosen look similar, some are unique.
Great work, good luck!
1. When someone enters "1 / 3" how many decimal places you display in the result? My approach: use MAX(4, MAX(decimal_places(entered_values))). His approach: use 3 everywhere.
- Bonus 1: how many decimal places you display when someone enters "sin(3.14)"? What about "sin(1 / 3)"? My approach: use as much space you have on the screen.
- Bonus 2: how do decimal places propagate when you're using refs?
2. What to do when someone taps "=" on the expression where we already have a result? Chinese $2 hardware calculator approach: redo the last operation. My approach: do nothing. Tydlig's approach: insert last result as a ref.
3. What to do when someone enters huge numbers? My approach: trim them to the width of the screen, clearly displaying that, but keep the full figure when doing copy/paste or export to text. His approach: start using E-notation somewhere around 16th figure.
4. In an app like this there's a temptation to stop using cursor because calculators don't have it and you want to be backwards compatible with them. When you create a ref, how to make sure the destination of the ref is at the right position in the expression without introducing a cursor? I.e. how to make sure you're not getting "2 + 3 [ref] + 12" (you need an operator before "[ref]")? My approach: use a semi-rigid table, where operators are separated from operands. Tydlig's approach: use a little cursor, a part of the app I don't like, because your finger normally would block the cursor.
I can go on and on. Math-related stuff is hard.
The switching to scientific notation around x · 10¹⁶ hints at using IEEE 754 doubles underneath. I wonder what they are using underneath for the math functions (they make it sound like it's custom-built). I spent a while in uni porting math function implementations from C to Java for a simulations framework and noticed that they usually all have the same pattern of selecting many different ways of calculating the result based on the intervals of the operands (to more or less guarantee 15 digits of precision instead of 0–15 as would otherwise be the case).
I always imagined that if you were aiming for the mathematician market (huge market!!1 /s) you could have an app like that except on a tablet you'd use with a pen. Then you'd just write down calculations and OCR would figure out what you are trying to calculate and do the number crunching (where applicable), and intelligently recognise variables and a lot of different mathematical functions (I just don't like the whole process of going back and forth between my TI and my legal pad). That'd be a mathematician's (or just mine) wet dream.
http://www.youtube.com/watch?v=RZKjc4Rzm2Y
But it doesn't do any of the number crunching, mathematical work.
Scalar does not deal with plain text as math. At all. Plain text is good on Macs with keyboard as it allows very quick, familiar and intuitive copy/paste and document restructuring, but is terrible on touch screens. That was the main motivation for me to start the project, BTW.
Commenting system is different as well (Soulver simply ignores all non-parseable text).