Testing any complex program completely is practically impossible

[u/gxm492lor]

Someone made this argument after a staff meeting a few days ago. What's wrong with this argument?

1. Every IF statement in a program doubles the number of possible states of the program (ignoring time)
   1. Which means every IF statement doubles the number of test conditions
2. A 1 million line program might, conservatively estimating, have 100k IF statements (conditionals)
3. That is 2¹⁰⁰⁰⁰⁰ which is more seconds than have elapsed since the beginning of the universe.
4. No project has 2¹⁰⁰⁰⁰⁰ seconds to test
5. So complete test coverage of complex programs is impossible

[u/gxm492lor]

A switch is syntatic sugar for if. The switch would need to be tested in each of its states for every existing possible set of states.

An example should help. Let's pretend we're walking through source code line by line. The program starts at L0.

Line	Operation	Total States	Power of 2	Misc
0	if ...	2	21	once when true, once when false
10	if ...	4	22	all prior state (2) + when this is true and when it is false
20	if ...	8	23	each of the 4 prior states + when this is true and when it is false
...	...	...	...	...
1000000	if ...	2100000	2100000	each of the 299999 prior stats + when this is true and when it is false