[PATCH] D48661: [Fixed Point Arithmetic] Fixed Point Constant

[Bevin Hansson via Phabricator via cfe-commits]

ebevhan added inline comments.


================
Comment at: lib/Basic/FixedPoint.cpp:53
+    // We can overflow here
+    unsigned ShiftAmt = DstScale - Scale;
+    if (Val < 0 && Val.countLeadingOnes() >= ShiftAmt)
----------------
ebevhan wrote:
> I think saturation can be modeled a bit better. It should be possible to do the overflow check/saturation once instead of twice, and also have it fit in better with the other conversions.
> 
> Saturation on a value is essentially checking whether all bits above and including a certain bit are all the same, and 'clamping' to either the minimum (the mask) or maximum (inverse of the mask) if not.
> ```
> // Saturate Value to SatWidth. This will clamp Value at the signed min/max of a value that is SatWidth long.
> Saturate(SatWidth):
>   Mask = highBits(Width, SatWidth + 1)
>   Masked = Value & Mask
>   Result = Value
>   if (Masked == Mask || Masked == 0) {
>     if (Masked.isNegative())
>       Result = Mask
>     else
>       Result = ~Mask
>   }
> ```
> This cannot be done on the value in the source scale, since upscaling after clamping would produce an incorrect value - we would shift in 0's from the right even though we should have saturated all bits completely. Also, we cannot upscale without first extending or we might shift out bits on the left that could affect saturation.
> 
> One thing to note is that (I'm ***pretty sure*** this is the case) fractional bits cannot affect saturation. This means that we can find a common scale, then perform the saturation operation, and then resize, and the value should just fall into place. Basically:
>   # Upscale if necessary, but extend first to ensure that we don't drop any bits on the left. Do this by resizing to `SrcWidth - SrcScale + std::max(SrcScale, DstScale)` and then upscaling normally by `DstScale - SrcScale`.
>   # Downscale if necessary by `SrcScale - DstScale`. (I think; in our downstream, we saturate first and then downscale, but we also assume that saturation can only occur on _Fract, and doing saturation first makes the saturation width calculation a bit messier because it will be a `max` expression. I'm unsure if the order can be changed.)
>   # At this point, the scale of the value should be `DstScale`. Saturate with `Saturate(DstWidth)`.
>   # Now the value should be in range for the new width, and will be at the right scale as well. Resize with `extOrTrunc(DstWidth)`.
>   # (Also; if the result was negative and the dest type is unsigned, just make the result zero here instead.)
> 
> Note that the order of operations is different than what I've mentioned before with non-saturated conversion (downscale if needed, resize, upscale if needed), but it works because we only do the upscale as a resize+upscale. Somewhere in here you also need to change the signedness of the value, but I'm not entirely certain where. Likely after 4.
> 
> Everything I've mentioned here is semi-conjectural, since our implementation has different type widths than the defaults in this one, we can only saturate on _Fract, and our unsigned types have padding. It's possible that there are some assumptions that cause this method to fail for unsigned without padding, or perhaps for some other type conversion, but I haven't come up with a counterexample yet.
Now that I think about it a bit more, it's clear that the Saturate routine does not work for unsigned fixed-point without padding. That would need to be taken into consideration, but the rest should work.


Repository:
  rC Clang

https://reviews.llvm.org/D48661