Re: Help with Hand-Optimized Assembly

[Terje Mathisen]

James Van Buskirk wrote:
> "Bill Woessner"<woessner@nospicedham.gmail.com>  wrote in message
> 67ddafac-ae03-4ef1-b156-5488e8b8086a@i26g2000vbt.googlegroups.com">news:67ddafac-ae03-4ef1-b156-5488e8b8086a@i26g2000vbt.googlegroups.com...
>
> > This compiles, runs and produces the correct answers.  But I have a
> > few issues with it:
>
> > 1) If I declare this function inline, it gives me garbage (like
> > 10^-304)
> > 2) If I compile with -Wall, I get a warning that the function doesn't
> > return a value, which is absolutely true, but I don't know how to fix
> > it.
> > 3) I don't like how TWO_PI and NEG_TWO_PI are defined.  I had to steal
> > it from some generated assembly.  It would be nice to use M_PI,
> > 4*atan(1) or something like that.
>
> I can't help you with your questions because I would always write
> something like this in assembly rather than C, but is there some
> reason that you can't use SSE2 rather than x87 here?  SSE2 should
> be much faster if available in the context of your problem.

I'll second James' suggestion about SSE2!

Anyway, it seem that what you are trying to do is to take the difference 
between two angles and then make sure that said difference will be in 
the [-pi .. pi> range, right?

I.e. what is the rotation angle to get from theta2 to theta1?

Let's start by looking at the various alternatives:

if the signs of th1 and th2 are the same, then the difference _must_ be 
in range:

 0 - pi = -pi
 pi - 0 = pi

 -0 - -pi = pi
 -pi - 0  = -pi

It is only when the signs differ that you might need to add or subtract 
2pi to bring it into range:

 pi - -pi = 2pi
-pi - pi = -2pi

I don't see immediately how I can use this to speed it up though...

Anyway, trying your original algorithm:

  movq xmm0,[theta1]

  subsd xmm0,[theta2]   ;; Result in [-2pi to 2pi]
  movq xmm2,[plus_mask] ;; 0x7fffff...

  andpd xmm2,xmm0       ;; ABS(diff), [0 to 2pi]
  movq xmm3,[pi]

  cmplesd xmm3,xmm2     ;; -1 mask if diff > pi
  andpd xmm3,[twopi]    ;; 0 or 2pi
  subsd xmm2,xmm3       ;; [-pi to pi]

If the original subtraction sign was negative, then we must invert the 
sign of the result:

  andpd xmm0,[signbits] ;; (-0.0 , -0.0)
  xorpd xmm0, xmm2

The code can be rescheduled a bit, and the mixture of 64-bit scalar and 
128-bit packed operations must be checked that they don't introduce 
forwarding problems, but it seems like it should run in 10-15 cycles, 
depending upon the latency of the FP operations (SUBSD, CMPLESD, SUBSD)

I tried to figure out a way to use scaling and integer math, but that is 
likely to be slower.

Terje
--
- <Terje.Mathisen at tmsw.no>
"almost all programming can be viewed as an exercise in caching"