Fast partitioned sum could be more general

[rikedyp]

The fast partitioned sum does not return the same results as +/¨⍺⊂⍵ if ⍺ does not start with a 1

      0 1 0 1 0 0 0 {¯2-⌿0⍪(1⌽⍺)⌿+⍀⍵} 1 3 2 4 4 4 4
1 5
      0 1 0 1 0 0 0 {+/¨⍺⊂⍵} 1 3 2 4 4 4 4
5 16

This can be rectified with some conditional modification of the partition vector

      0 1 0 1 0 0 0 {¯2-⌿(0/⍨⊃⍺)⍪(1@(≢⍺)⊢1⌽⍺)⌿+⍀⍵} 1 3 2 4 4 4 4
5 16

[abrudz]

{¯2-⌿(0/⍨⊃⍺)⍪(1⌽1@1⊢⍺)⌿+⍀⍵} is better but it is very rare to actually need this, and it makes the code much more involved (though at next to no performance cost). I think it better to stipulate that all the fast partitioned algorithms require Av beginning with 1.

[rikedyp]

Yeah I agree, the original is much simpler. Might be nice to add comments to aplcart examples.
Here is a prototype format: APLCart description in the header, main example in code, comments in the footer:

TiO flat partitioned sum example