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[Bug-apl] Supporting negative ranks for ⍤ operator

From: Elias Mårtenson
Subject: [Bug-apl] Supporting negative ranks for ⍤ operator
Date: Wed, 27 Apr 2016 15:28:46 +0800

Dyalog supports the use of a negative rank parameter, while GNU APL does not. Instead GNU APL follows the ISO spec which says that a negative value should be clamped to 0.

However, the Dyalog model is quite useful. Here's how it's described in their documentation:

“The Rank operator ⍤ 1 applies function f successively to the sub-arrays in Y specified by k. If k is positive, it selects the k-cells of Y. If k is negative, it selects the (r+k)- cells of Y where r is its rank. If k is ¯1 it selects the major cells of Y.”

I think it seems reasonable to adapt this to GNU APL as well?

About the ISO specification of ⍤

In writing the above message, I was reading the ISO specification for the rank operator, and I find it incredibly confusing. I have quoted the description below, and based on my reading of this text, the rank parameter is not just a single value, but can be up to three values. However, no matter how I read it, I still can't see how any but the the very first value is actually every used.

Also, the case where LENGTH ERROR is supposed to be raised does not happen in GNU APL.

It seems as the specification for the rank operator is just broken on several levels in the spec. That seems to me to be reason enough to not pay attention to the spec in this case and just adapt the way Dyalog does it.

Here's the spec for the rank operator from the ISO spec:

Informal Description:
The result of f⍤y is a function which, when applied to B, returns Z, the result of applying the function f to the rank-y cells of B.

Evaluation Sequence:
If y is a scalar, set y1 to ,y. Otherwise set y1 to y.
If y1 is not a vector, signal domain-error.
If y1 has more than three elements, signal length-error.
If any element of y1 is not a near-integer, signal domain-error.
Set y2 to ⌽3⍴⌽y1.
Set y3 to the first-item in y2.
Set y4 to the integer-nearest-to y3.
If y4 exceeds the rank of B, set y5 to the rank of B, otherwise set y5 to y4.
If y5 is negative, set y6 to 0⌈y5 plus the rank of B, otherwise set y6 to y5.
Apply f to the rank-y6 cells of B.
Conform the individual result cells. Let their common shape after conforming be q, and let p be the frame of B with respect to f, that is, (rank of B) minus y6, and
return the overall result with shape p,q.

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