1
00:00:00,025 --> 00:00:02,900
Okay, so now we're going to answer the question. So if we want

2
00:00:02,900 --> 00:00:06,520
to consider all these inputs, and run them all on the software,

3
00:00:06,520 --> 00:00:09,490
let's see how it will work. Let's assume that these are, 32

4
00:00:09,490 --> 00:00:12,280
bit integers. So at this point what we will have is, a

5
00:00:12,280 --> 00:00:15,130
number of combination, which is 2 to the 32, times 2 to

6
00:00:15,130 --> 00:00:18,390
the 32. They're two integers. This is equal to 2 to the

7
00:00:18,390 --> 00:00:21,910
64, which in turn, is more or less equal, to 10 to

8
00:00:21,910 --> 00:00:25,110
the 19. So 10 to the 19 is the number of tests that

9
00:00:25,110 --> 00:00:27,960
we need to run to cover the whole domain. Now let's assume

10
00:00:27,960 --> 00:00:31,400
that we can run one test per nanosecond. So what that means

11
00:00:31,400 --> 00:00:34,290
is that we can run 10 to the 9 tests per second,

12
00:00:34,290 --> 00:00:37,240
and that's a lot. If we do the math, that results in 10

13
00:00:37,240 --> 00:00:40,750
to the 10 seconds over all, because we have 10 to the

14
00:00:40,750 --> 00:00:43,760
19 tests, we could run 10 to the 9 tests per second

15
00:00:43,760 --> 00:00:46,630
so, we do the math, and we can run all these tests

16
00:00:46,630 --> 00:00:50,340
in 10 to the 10 seconds. And what that corresponds to, it's about

17
00:00:50,340 --> 00:00:54,470
600 years, so a lot of time. So even for such

18
00:00:54,470 --> 00:00:57,710
a simple problem, a problem that takes two integers and adds them,

19
00:00:57,710 --> 00:01:00,990
it will take more than 500 years to test it exhaustively. So

20
00:01:00,990 --> 00:01:04,690
the bottom line here is that we just can't do exhaustive testing.