[sdiy] Accuracy with integer maths

Robyn Mayol rominbayol at gmail.com
Tue Feb 4 16:06:06 CET 2014

The link should be


Thank you!

> Tom, 
> Everything I know I wrote down here: 
> http://blog.credland.net/2013/09/binary-fixed-point-explanation.
> Does that help? 
> What are you doing the maths on?  
> On Tue, Feb 4, 2014, at 02:00 PM, Tom Wiltshire wrote:
>> Hi All,
>> Does anyone know any good websites where I can learn about accuracy
>> requirements in integer maths?
>> Specifically, I'd like to know how many bits I need to calculate for
>> various algorithms; multiplication, interpolation, etc.
>> I've been doing some experiments and they suggest to me that I need more
>> bits than I'd expected to eliminate errors. For example, if I take two
>> 8-bit integers and multiply them, I get a 16-bit result. If I'm only
>> interested in (say) the top 10 bits of that result, do I need to
>> calculate the full 8x8 multiplication? Can I eliminate some of the
>> calculation without getting any errors?
> There are all sorts of tricks you can do to make this faster and easier.
> It's very architecture dependent though.  For example, the
> multiplication instruction on a CPU might use two registers for the
> result and you can just discard one of them.  
>> What about if I needed 12 bits? Or what about if I were treating one
>> 8-bit value as a 0 -> 0.99 amount value, and I multiply by the other
>> 8-bit value and then use only the top 8 bits of the result.
>> If anyone knows anywhere where there is a clear, programmer-orientated
>> explanation of this sort of stuff, I'd be grateful. A serious academic
>> number-theory treatment probably won't get through to me, since I'm not a
>> (remotely!) serious academic or a number theoretician.
>  Jim Credland
>  jim at cernproductions.com
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