comparing speed, efficiency, etc, in specs

[rem736]

does anyone else get annoyed when a manufacturer (such as apple) compare the speed of a new device with the same device of the previous generation and uses "2X faster" to describe the improvements?

here's the logic.

when they say 30% faster (or anything less than 100%), it is accurate. example, previous gen device runs at 100 MHz, new device runs at 130 Mhz. this is accurately described as 30% faster. translated to decimals, 30% is 0.30.
40% faster is 0.40, 50% is 0.50...99% is 0.99. so logically at 100% faster, it's 1.0 faster.

but then when a device is running at 200 MHz compared to something running at 100 MHz, they say it's 2X faster. what happened to 1X faster?
they can say twice as fast, but 2X faster is completely wrong.

[guanaco]

The paragraph starting "when they say..." is wrong. If the old device runs at 100 MHz and the new device runs at 130 MHz, the speed-up is described indeed as 30% faster. But translated to decimals, 30% faster is not 0.30, it is 1.30. Why? the answer is because 100 * 1.30 = 130.

The speed-up formula is S = new / old. Thus, in the example above, S = 130 / 100 = 1.30, that is 30% faster.

100% faster is not 1.0 faster, is 2.0 faster. For example, if old device runs at 100 MHz and new device is 200 MHz, then S = 200 / 100 = 2.0, that is 100% faster.

2X faster means the new device is 2 times faster, that is 100% faster.

1X faster means the 2 devices have the same speed. For example, if both devices runs at 100 MHz, then S = 100 / 100 = 1.

If all these sounds exotic, please see the section 1.6 of "Computer Organization and Design" by Patterson and Hennessy. There is a nice discussion about performance and how to measure it.