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Fri May 17 17:20:16 EDT 2019

accumulation

i:
   Ai <- A(i-1) + Bi

This notation abstracts the need to initialize the accumulator before
the loop starts.

Representing accumulators is important, so maybe it is possible to
generalize:

i:
   A_i <- A_f(i) + B_i

There based on what A_f(i) is, we can implement it as a single
accumulator, a finite set of accumulators (a shift register), or a
full array.


So that is all fluff.  Let's use i' as the previous index, with
implicit initialization.

Actually I don't have any way to use the two types of references:
previous accumulator value and final, after the loop.

i:
  A <- A Bi
i:
  Di <- A Ci

So it appears that accumulators need some special notation.  To make
it work for triangle patterns, use the triangle notation.


i:
  Ai <- Ai1 Bi
i:
  Di <- AI Ci

Where I is the last element that was stored in the array in its
constructing loop.




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