fixed point is taught wrong.
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@Rk yes, fixed point requires a lot of thinking about your exact problem domain and what the limits are before overflow occurs
which is why it's so vexing that it's usually explained so poorly because you can get way better results by having many different fixed point types with different bit layouts for different tasks, precisely so you can avoid overflow
but mixing different types is basically never explained
@eniko some years ago i helped with a project in a low energy context: once in a while a sensor would trigger an interrupt, waking up the device. not all the wake ups needed an action, to figure it out you would need to do a bunch of non linear calculations and react accordingly. using floats pushed the device over the maximum energy consumption, as it was powered with non rechargeable caps. fixed point math with an iterative solver outperformed fp, doubling the expected life of the device.
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@eniko some years ago i helped with a project in a low energy context: once in a while a sensor would trigger an interrupt, waking up the device. not all the wake ups needed an action, to figure it out you would need to do a bunch of non linear calculations and react accordingly. using floats pushed the device over the maximum energy consumption, as it was powered with non rechargeable caps. fixed point math with an iterative solver outperformed fp, doubling the expected life of the device.
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@eniko sometimes the old techniques are the appropriate ones. too bad juniors are actively told that dealing with bits and low level concepts is not relevant and 'premature optimizaiton'. one of my clients has engineers with a terrible fear of exoteric concepts such as 'bit masks'... such is life!
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fixed point is taught wrong. instead of saying "to multiply two fixed point values you have to multiply them then shift them back into position" what it really should be is "when you multiply two fixed point values the result has a fractional precision in bits equal to the sum of the fractional precision of the two fixed point types multiplied"
@eniko Teaching shifting as if it were fundamental to fixed point seems strange to me. My attempt to explain it back in 2020: “Multiplication works as expected too, but the product contains twice the number of bits. Multiplying two Q4.4 numbers results in a Q8.8 product” - https://projectf.io/posts/fixed-point-numbers-in-verilog/
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this also makes it easier to see that if you're transforming a fixed point type into another fixed point type via multiplication (like position * position = edgeweight for a rasterizer) you may want to not shift at all if you want the resulting fixed point type to represent the transformation precisely without any rounding
@eniko I think often I've seen fixed point multiplication as being from X:Y * X:Y = X:Y, ie same precision. Increasing precision of the result means actually changing the type (which is ok like you say) but it is another operation. Maybe that is where the confusion come from from places that describe it. I like your view of it of course and it builds intuition.
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@gabrielesvelto i've read about fixed point math many times on the modern internet and i don't think i've ever seen this pointed out. i had to come to it on my own and it's not super intuitive
@eniko @gabrielesvelto I seem to remember the "Graphics Gems" series of books containing a lot of great information on fixed point maths, including various useful algorithms. Unfortunately I'm pretty sure those books are long out of print (exorbitant prices anyway) - I read them at our university library over 20 years ago.
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@eniko @gabrielesvelto I seem to remember the "Graphics Gems" series of books containing a lot of great information on fixed point maths, including various useful algorithms. Unfortunately I'm pretty sure those books are long out of print (exorbitant prices anyway) - I read them at our university library over 20 years ago.
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undefined oblomov@sociale.network shared this topic
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fixed point is taught wrong. instead of saying "to multiply two fixed point values you have to multiply them then shift them back into position" what it really should be is "when you multiply two fixed point values the result has a fractional precision in bits equal to the sum of the fractional precision of the two fixed point types multiplied"
@eniko one would expect that anyone familiar with hand calculations like long multiplication would be aware of that … aren't these things taught in like primary school?
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@eniko one would expect that anyone familiar with hand calculations like long multiplication would be aware of that … aren't these things taught in like primary school?
@oblomov you still do a lot of long multiplication/division? Cause I haven't in 30 years
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@oblomov you still do a lot of long multiplication/division? Cause I haven't in 30 years
@eniko I have kids
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@eniko I have kids
@oblomov lol fair enough
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@oblomov lol fair enough
@eniko in fact, I'm moderately pissed that they don't teach the digit-by-digit square root algorithm (which is similar to long division) anymore so I haven't had an opportunity to refresh that.
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