Quick alternatives to floating point multiplication to calculate percentages

Question

I'm writing some code on an Arduino that needs to run fast and make rough approximations to percentages of integers.

For example, given a number I want to find 90% of it, or 70% or 30% etc. The obvious way to do it is multiply by a floating point eg. x * 0.9; or x * 0.3; But because I need speed, I want to avoid a floating point calculation. If I was just dividing by a power of two, I'd do a bitwise shift, but are there similar techniques for approximating 90%, 80% etc. using integers?

Mysticial · Answer 1 · 2012-01-14T02:26:37.500

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You can approximate those percentages with fractions that have a power-of-two denominator.

Here's a simple example with 2^16:

90% = 90 / 100 ~ 58982 / 65536
70% = 70 / 100 ~ 45875 / 65536
30% = 30 / 100 ~ 19661 / 65536

 x% =  x / 100 ~ x * 655 / 65536

The divisions (which are now powers-of-two) can be done with shifts.

Of course, it may take some pre-computation to generate those fractions.

edited Jan 14 '12 at 02:26

answered Jan 14 '12 at 02:21

Mysticial

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Ah ... that looks promising. So x% of y is (y * x * 655 / 65536) ? – interstar Jan 14 '12 at 03:55
Yes, that's correct. `2^16` should be accurate enough. If you need more precision you can always use something larger than `2^16`. – Mysticial Jan 14 '12 at 03:59
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You also try `(y * x * 655 + 32768) / 65536` if you want it to round better. – Mysticial Jan 14 '12 at 04:01

score 2 · Answer 2 · edited May 23 '17 at 10:27

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Bit shifting How can I multiply and divide using only bit shifting and adding?

You can use bit shifting for to multiply and divide arx example x = (x*9)/10

As for a code example, if you get stuck I could try and burn some brain cells to work it out. Just ask :)

edited May 23 '17 at 10:27

Community

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answered Jan 15 '12 at 11:56

Hellonearthis

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Quick alternatives to floating point multiplication to calculate percentages

2 Answers2