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# Fast list-product sign for PackedArray?

As a continuation of my previous question, Simon's method to find the list product of a PackedArray is fast, but it does not work with negative values.

This can be "fixed" by `Abs` with minimal time penalty, but the sign is lost, so I will need to find the product sign separately.

The fastest method that I tried is `EvenQ @ Total @ UnitStep[-lst]`

```lst = RandomReal[{-2, 2}, 5000000]; Do[ EvenQ@Total@UnitStep[-lst], {30} ] // Timing Out[]= {3.062, Null} ```

Is there a faster way?

This is a little over two times faster than your solution and apart from the nonsense of using `Rule@@@` to extract the relevant term, I find it more clear - it simply counts the number elements with each sign.

```EvenQ[-1 /. Rule@@@Tally@Sign[lst]] ```

To compare timings (and outputs)

```In[1]:= lst=RandomReal[{-2,2},5000000]; s=t={}; Do[AppendTo[s,EvenQ@Total@UnitStep[-lst]],{10}];//Timing Do[AppendTo[t,EvenQ[-1/.Rule@@@Tally@Sign[lst]]],{10}];//Timing s==t Out[3]= {2.11,Null} Out[4]= {0.96,Null} Out[5]= True ```

A bit late-to-the-party post: if you are ultimately interested in speed, `Compile` with the C compilation target seems to be about twice faster than the fastest solution posted so far (`Tally` - `Sign` based):
```fn = Compile[{{l, _Real, 1}}, Module[{sumneg = 0}, Do[If[i < 0, sumneg++], {i, l}]; EvenQ[sumneg]], CompilationTarget -> "C", RuntimeOptions -> "Speed"]; ```
```In[85]:= lst = RandomReal[{-2, 2}, 5000000]; s = t = q = {}; Do[AppendTo[s, EvenQ@Total@UnitStep[-lst]], {10}]; // Timing Do[AppendTo[t, EvenQ[-1 /. Rule @@@ Tally@Sign[lst]]], {10}]; // Timing Do[AppendTo[q, fn [lst]], {10}]; // Timing s == t == q Out[87]= {0.813, Null} Out[88]= {0.515, Null} Out[89]= {0.266, Null} Out[90]= True ```