# PageRank

In this section, you will learn about the following components in Spatial:

• Sparse transfers to DRAM

Note that a large collection of Spatial applications can be found here.

## Overview

The PageRank algorithm was historically a core component of Google’s search algorithm that decides how to sort search results. It was named after Larry Page, one of the co-founders of Google.

In this tutorial, we use it as an example of how to work with sparse data structures. The algorithm uses a sparse graph that encodes connections between nodes. Each node contains its own “rank,” and by iteratively traversing the graph and updating the ranks of nodes based on the ranks of their neighbors, we converge on a fixed set of ranks for all nodes.

## Basic implementation

``` @spatial object PageRank extends SpatialApp {
override def runtimeArgs: Args = "50 0.125"

type Elem = FixPt[TRUE, _16, _16] // Float
type X = FixPt[TRUE, _16, _16] // Float

/*
Currently testing with DIMACS10 Chesapeake dataset from UF Sparse Matrix collection

*/
val margin = 0.3f

def main(args: Array[String]): Unit = {
val tileSize = 16
val sparse_data = loadCSV2D[Int](s"\$DATA/pagerank/pagerank_chesapeake.csv", " ", "\n").t
val rows = sparse_data(0, 0)
val node1_list = Array.tabulate(sparse_data.cols - 1) { i => sparse_data(0, i + 1) - 1 } // Every page is 1-indexed...
val node2_list = Array.tabulate(sparse_data.cols - 1) { i => sparse_data(1, i + 1) - 1 } // Every page is 1-indexed...
// Preprocess to get frontier sizes.  We can do this on chip also if we wanted
println("Matrix has " + rows + " rows")
val edgeLens = Array.tabulate(rows){ i =>
Array.tabulate(node1_list.length){ j => if (node1_list(j) == i) 1 else 0 }.sum
}
val edgeIds = Array.tabulate(rows) { i =>
var id: Int = -1
Array.tabulate(node1_list.length) { j =>
if (id == -1 && node1_list(j) == i) {
id = j
j
} else {
0
}
}.sum
}
printArray(edgeLens, "edgeLens: ")
printArray(edgeIds, "edgeIds: ")

val par_load = 1
val par_store = 1
val tile_par = 1
val page_par = 2

val itersIN = args(0).to[Int]
val dampIN = args(1).to[X]

val iters = ArgIn[Int]
val NP = ArgIn[Int]
val damp = ArgIn[X]
val NE = ArgIn[Int]
setArg(iters, itersIN)
setArg(NP, rows)
setArg(damp, dampIN)
setArg(NE, node2_list.length)

val OCpages = DRAM[X](NP)
val OCedges = DRAM[Int](NE) // srcs of edges
val OCedgeLens = DRAM[Int](NP) // counts for each edge
val OCedgeIds = DRAM[Int](NP) // Start index of edges

val pagesInit = Array.tabulate(NP) { i => 4.to[X] }

setMem(OCpages, pagesInit)
setMem(OCedges, node2_list)
setMem(OCedgeLens, edgeLens)
setMem(OCedgeIds, edgeIds)

Accel {
Sequential.Foreach(iters by 1) { iter =>
// Step through each tile
Foreach(NP by tileSize par tile_par) { page =>
val local_pages = SRAM[X](tileSize).buffer
val local_edgeIds = SRAM[Int](tileSize)
val local_edgeLens = SRAM[Int](tileSize)
val pages_left = min(tileSize.to[Int], NP - page)
local_pages load OCpages(page :: page + pages_left par par_load)
local_edgeLens load OCedgeLens(page :: page + pages_left par par_load)
local_edgeIds load OCedgeIds(page :: page + pages_left par par_load)
// Process each page in local tile
Sequential.Foreach(pages_left by 1 par page_par) { local_page =>
// Fetch edge list for this page
val edgeList = FIFO[Int](128)
val id = local_edgeIds(local_page)
val len = local_edgeLens(local_page)
edgeList load OCedges(id :: id + len)
// Triage between edges that exist in local tiles and off chip
val nearPages = FIFO[Int](128)
val farPages1 = FIFO[Int](128)
val farPages2 = FIFO[Int](128)
Foreach(edgeList.numel by 1) { i =>
val tmp = edgeList.deq()
if (tmp >= page && tmp < page + pages_left) {
nearPages.enq(tmp - page)
} else {
farPages1.enq(tmp)
farPages2.enq(tmp)
}
}
// Fetch off chip info
val local_farPages = FIFO[X](128)
val local_farEdgeLens = FIFO[Int](128)
local_farPages gather OCpages(farPages1) // Need fifos 1 and 2 because fifo is consumed during gather
local_farEdgeLens gather OCedgeLens(farPages2)

// Do math to find new rank
val pagerank = Pipe.Reduce(Reg[X](0))(len by 1) { i =>
if (nearPages.isEmpty) {
println("page: " + page + ", local_page: " + local_page + " deq from far")
local_farPages.deq() / local_farEdgeLens.deq().to[X]
} else {
val addr = nearPages.deq()
println("page: " + page + ", local_page: " + local_page + " deq from near addr " + addr)
}
}{_+_}

// Write new rank
local_pages(local_page) = pagerank * damp + (1.to[X] - damp) / NP.value.to[X]
}
OCpages(page :: page + pages_left par par_store) store local_pages
}
}
}

val result = getMem(OCpages)

val gold = Array.empty[X](NP)
// Init
for (i <- 0 until NP) {
gold(i) = pagesInit(i)
}

// Really bad imperative version
for (ep <- 0 until iters) {
// println("Iter " + ep)
for (i <- 0 until NP) {
val numEdges = edgeLens(i)
val startId = edgeIds(i)
val iterator = Array.tabulate(numEdges) { kk => startId + kk }
val these_edges = iterator.map { j => node2_list(j) }
val these_pages = these_edges.map { j => gold(j) }
val these_counts = these_edges.map { j => edgeLens(j) }
val pr = these_pages.zip(these_counts){(p, c) => p / c.to[X] }.sum
// println("new pr for " + i + " is " + pr)
gold(i) = pr * dampIN + (1.to[X] - dampIN) / rows.to[X]
}
}

println("PageRank on DIMACS10 Chesapeake dataset downloaded from UF Sparse Matrix collection")
printArray(gold, "gold: ")
printArray(result, "result: ")
val cksum = result.zip(gold) { case (o, g) => (g < (o + margin.to[X])) && g > (o - margin.to[X]) }.reduce {
_ && _
}
println("PASS: " + cksum + " (PageRank)")
assert(cksum)
}

}
```

The example to the left demonstrates one way to write PageRank in Spatial.

We run this algorithm for some number of iterations specified as an ArgIn.

We operate on a tile-worth of pages at a time. We fetch the information for all pages within this tile, and then we work locally on these pages.

In this loop, we iterate through each page in the tile individually. We collect the starting address of its edge list, and the number of edges it has. We then load this information as a dense transfer into `edgeList`.

We sort these connected nodes into pages that are already in local memory and those that are not. For those that are not in local memory, we must perform a `gather` operation to fetch them out of DRAM.

Apply update equation to the currently active page.

To compile the app for a particular target, see the Targets page