[VTR][Util] Added Prefix Sum Class

[AlexandreSinger]

A prefix sum is a classic data structure for quickly finding the sum of any sub-region of fixed N-Dimensional array of values. It pre-computes the partial sums of regions within an array and uses that information later to save time.

This is currently used in the net_cost_handler to pre-compute number of inter-die connections.

This class can be useful in other algorithms. For example, in a Partial Legalizer in an AP flow, it can allow for quick lookups into the capacity and utilization of regions on the FPGA.

Moved the Prefix Sum class from the net_cost_handler into the VTR Util.

[AlexandreSinger]

@vaughnbetz I needed to use a Prefix Sum in the new Partial Legalizer I am working on. Instead of writing a custom one for my use-case, I made a general class which can be found in the vtr_util library. I found that a Prefix Sum was already being used for 3D connections, I think written by @amin1377; so I wrapped that into this class. All tests are passing. Please review when you have a moment.

[vaughnb-cerebras]

Nice change! A couple of thoughts embedded.
I believe also use 1D prefix sums in the placer in case you want to also pull those out. See

vtr-verilog-to-routing/vpr/src/place/net_cost_handler.cpp

Line 154 in 5a22313

void NetCostHandler::alloc_and_load_chan_w_factors_for_place_cost_() {

[AlexandreSinger]

@vaughnbetz Thank you for your feedback on this! I did not realize that those were 1D Prefix Sums; I have created a class for PrefixSum1D and have converted them into using this class. I found that the original code was a little confusing with how it handled 0 channel widths, so I rewrote it slightly to make this more obvious. This does not change the functionality at all, just makes it more explicit that we assume the channel widths are at least 1.

[vaughnb-cerebras]

Thanks, LGTM!

[AlexandreSinger]

Cool! Ill merge when it passes CI.