italie |
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Programming/maths question....soft floats...
#312003 - 07/26/13 02:21 PM
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Torn in my head on how to handle an issue. I have many things to consider (timing, memory, volume of code additions, etc) that are jumbling the way I'm looking at this issue. Curious on how some of the more seasoned vets would tackle this one, or if someone would set up the math different.
The goal:
A simple ratio(ish) equation where I take points A, B and C in a data plot, and perform the equation "(A/C) / (B/C)". I need to keep at least two significant digits worth of precision.
example values might be 15034, 15044, 15157 (A,B,C)
The issue:
I'm working with an embedded processor that only does soft floats. Not only is this time consuming, but works out the correct answer only 75% of the time. Other times I see "rounding errors" (assuming they are rounding errors int he soft float libs) which slightly skew my two significant digits.
No matter how I play with the numbers, precision, ect, as long as floats are involved I get the occasional glitch. Thinking of adding fixed point libs, but that is going to be a pretty large hit for a tiny issue.
Thoughts, comments? I'm working on six different issues at the moment, and I can't seem to clear my head on this one...
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GatKong |
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Tetris Mason
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Re: Programming/maths question....soft floats...
[Re: italie]
#312004 - 07/26/13 02:56 PM
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For starters (A/C)/(B/C)=A/B
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| Gor |
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Giver of truth.
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Re: Programming/maths question....soft floats...
[Re: GatKong]
#312007 - 07/26/13 03:52 PM
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> For starters (A/C)/(B/C)=A/B
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Oh for Pete's sake.
loser.com
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| italie |
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MAME owes italie many thank yous, hah
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Re: Programming/maths question....soft floats...
[Re: Gor]
#312009 - 07/26/13 04:14 PM
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> > For starters (A/C)/(B/C)=A/B
Okay okay....piss poor example aside, maybe i can clarify a little later when I get home on a real PC.
Trying to ask a specific question without giving up a specific code sample sucks..
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Re: Programming/maths question....soft floats...
[Re: italie]
#312016 - 07/26/13 06:31 PM
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Fixed point isn't particularly hard to do as long as you have extended precision multiply/divide. Lacking that it's a bitch. As long as each argument has the same precision, add/subtract/compare are all just like doing the operation on integers. Multiply requires you to do an extended precision multiply, then adjust and truncate the result, and divide requires you to extend and adjust the dividend, then divide and truncate the result. It's easier and more reliable than bringing floats into it.
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Re: Programming/maths question....soft floats...
[Re: italie]
#312017 - 07/26/13 07:50 PM
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As for keeping "significant digits": if you mean keeping decimal digits, you definitely should see this: http://floating-point-gui.de/
As for dividing without a division instruction: see this: http://www.math.usm.edu/lambers/mat460/fall09/lecture10.pdf
If you are working on integers, and want the result as a percentage, you don't need soft floats. You can compute (A/B) as ((100*A)/B) and have your answer as a percentage. If you want to round to the nearest percentage point, compute (A/B) as ((((200*A)/B)+1)/2) or maybe ((((200*A)/B)+1)>>1) where >> is binary right-shift.
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Re: Programming/maths question....soft floats...
[Re: italie]
#312021 - 07/26/13 09:53 PM
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If code size is a real consideration then I would say 'pick your battle'.
Find the bit that is destroying the most precision and then just use fixed point there and then convert it back.
My rule of thumb even with full floating point precision is 1 decimal of lost precision confidence per operation. Not always true but usually close enough.
I would probably 64bit int it (even if it cost a bunch more instructions/memory) shift it and then integer mul/div it then shift it back then drop it back into the float with a round so the rest of the code is ok.
Even that may not be 'ok' depending on how many operations you do. Pretty much for divides think about it as 1 number you cant trust anymore. For multiplies you need 2x the space. You can reduce the error by limiting your inputs. Instead of for example 2 8 bit vals multiplied together can in theory fill a 16 bit value. But by limiting them to 0-15 (4 bits) each you still fit in the 8 bit.
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Re: Programming/maths question....soft floats...
[Re: italie]
#312029 - 07/26/13 10:55 PM
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Some thoughts/questions...
Is there any way to use a lookup table to simplify the math?
Are the input values limited to specific values or a limited range?
What kind of rounding/truncation are you using? http://en.wikipedia.org/wiki/Rounding
My gut says that some sort of a custom fixed point implementation might be the best course of action. For example, when dealing with money, it's often easiest to work in cents, using an implied decimal point rather than working with dollars and fractional dollars.
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MAME owes italie many thank yous, hah
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Thanks for all the suggestions....
[Re: italie]
#312034 - 07/27/13 12:44 AM
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It sucks having to try and work through a difficult issue, without being able to just drop the actual code slice here for review. You guys got me thinking, and I think I have a viable stop-gap until some hardware changes are made in a few months.
The issue was indeed being caused by the IDE/embedded soft-float libs. Looks like they had some major issues fixed in recent versions. Pushed the math out to 64 bits and avoided float for the time. (This required me to alter a whole slew of external data, but it's the only way I'm getting anything close to reliable.)
Looks like the new hardware coming in will be a bit of an upgrade with an FPU...
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MAME owes italie many thank yous, hah
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Re: Programming/maths question....soft floats...
[Re: amused]
#312035 - 07/27/13 12:50 AM
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> As for keeping "significant digits": if you mean keeping decimal digits, you
> definitely should see this: http://floating-point-gui.de/
>
> As for dividing without a division instruction: see this:
> http://www.math.usm.edu/lambers/mat460/fall09/lecture10.pdf
>
> If you are working on integers, and want the result as a percentage, you don't need
> soft floats. You can compute (A/B) as ((100*A)/B) and have your answer as a
> percentage. If you want to round to the nearest percentage point, compute (A/B) as
> ((((200*A)/B)+1)/2) or maybe ((((200*A)/B)+1)>>1) where >> is binary right-shift.
Just curious for my own betterment, was significant digits not a term that carried across well?
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Re: Programming/maths question....soft floats...
[Re: italie]
#312039 - 07/27/13 04:52 AM
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