if 1000 has 33% increase=1333
2000 =2666
Yes, of course, you are correct, allowing for rounding, increasing 1000 by 33% is 1000 + 1000 * 33% = 1333 and increasing 2000 by 33% is 2000 + 200 * 33% = 2666.
Hmm, I'll try to explain;
1200MHz - 900Mhz = 300MHz
300Mhz / 900MHz = 33% -- so we say we have increased the processor frequency by 33%.
Also,
900MHz / 1200MHz = 75% -- so we say instructions will take only 75% as long to run.
So, for a fixed amount of work, we can calculate how long it will take to run. If a 2000 sigop transaction takes t amount of time on the 900MHz processor then we expect it to only take 0.75t on the faster one. There are potential hazards in this assertion. The software might not be strictly compute bound. Also, not every instruction will necessarily get the same advantage from the speedup, e.g. branches, etc.
*But* this does not indicate how much faster more work will run unless the software scales linearly with frequency. If the software does indeed scale linearly then the amount of time it takes to get a fix amount of work done will decrease linearly and the amount of work that can get done in the same amount of time will increase linearly.
For some unexplained (to me yet) reason, signature verification does not scale linearly. Instead it scales as the square;
| 1 | 1 |
| 2 | 4 |
| 3 | 9 |
| 4 | 16 |
| 5 | 25 |
| ... | ... |
| n | n² |
| ... | ... |
So, yes, one signature verification could indeed get done in 0.75t but 2000 will take 2000²*(0.75t).
Gosh, I am terribly sorry if I haven't explained this well.