# BlockDist¶

Usage

```use BlockDist;
```
class `Block`

This Block distribution partitions indices into blocks according to a `boundingBox` domain and maps each entire block onto a locale from a `targetLocales` array.

The indices inside the bounding box are partitioned "evenly" across the target locales. An index outside the bounding box is mapped to the same locale as the nearest index inside the bounding box.

Formally, an index `idx` is mapped to `targetLocales[locIdx]`, where `locIdx` is computed as follows.

In the 1-dimensional case, for a Block distribution with:

 `boundingBox` `{low..high}` `targetLocales` `[0..N-1] locale`

we have:

if `idx` is ... `locIdx` is ...
`low<=idx<=high` `floor(  (idx-low)*N / (high-low+1)  )`
`idx < low` `0`
`idx > high` `N-1`

In the multidimensional case, `idx` and `locIdx` are tuples of indices; `boundingBox` and `targetLocales` are multi-dimensional; the above computation is applied in each dimension.

Example

The following code declares a domain `D` distributed over a Block distribution with a bounding box equal to the domain `Space`, and declares an array `A` over that domain. The forall loop sets each array element to the ID of the locale to which it is mapped.

```use BlockDist;

const Space = {1..8, 1..8};
const D: domain(2) dmapped Block(boundingBox=Space) = Space;
var A: [D] int;

forall a in A do
a = a.locale.id;

writeln(A);
```

When run on 6 locales, the output is:

```0 0 0 0 1 1 1 1
0 0 0 0 1 1 1 1
0 0 0 0 1 1 1 1
2 2 2 2 3 3 3 3
2 2 2 2 3 3 3 3
2 2 2 2 3 3 3 3
4 4 4 4 5 5 5 5
4 4 4 4 5 5 5 5
```

Constructor Arguments

The `Block` class constructor is defined as follows:

```proc Block(
boundingBox: domain,
targetLocales: [] locale  = Locales,
dataParMinGranularity     = // value of  dataParMinGranularity      config const,
param rank                = boundingBox.rank,
type  idxType             = boundingBox.idxType,
type  sparseLayoutType    = DefaultDist)
```

The arguments `boundingBox` (a domain) and `targetLocales` (an array) define the mapping of any index of `idxType` type to a locale as described above.

The rank of `targetLocales` must match the rank of the distribution, or be `1`. If the rank of `targetLocales` is `1`, a greedy heuristic is used to reshape the array of target locales so that it matches the rank of the distribution and each dimension contains an approximately equal number of indices.

The arguments `dataParTasksPerLocale`, `dataParIgnoreRunningTasks`, and `dataParMinGranularity` set the knobs that are used to control intra-locale data parallelism for Block-distributed domains and arrays in the same way that the like-named config constants control data parallelism for ranges and default-distributed domains and arrays.

The `rank` and `idxType` arguments are inferred from the `boundingBox` argument unless explicitly set. They must match the rank and index type of the domains "dmapped" using that Block instance. If the `boundingBox` argument is a stridable domain, the stride information will be ignored and the `boundingBox` will only use the lo..hi bounds.

When a `sparse subdomain` is created for a `Block` distributed domain, the `sparseLayoutType` will be the layout of these sparse domains. The default is currently coordinate, but `LayoutCSR.CSR` is an interesting alternative.

Data-Parallel Iteration

A forall loop over a Block-distributed domain or array executes each iteration on the locale where that iteration's index is mapped to.

Parallelism within each locale is guided by the values of `dataParTasksPerLocale`, `dataParIgnoreRunningTasks`, and `dataParMinGranularity` of the respective Block instance. Updates to these values, if any, take effect only on the locale where the updates are made.

Sparse Subdomains

When a `sparse subdomain` is declared as a subdomain to a Block-distributed domain, the resulting sparse domain will also be Block-distributed. The sparse layout used in this sparse subdomain can be controlled with the `sparseLayoutType` constructor argument to Block.

This example demonstrates a Block-distributed sparse domain and array:

```use BlockDist;

const Space = {1..8, 1..8};

// Declare a dense, Block-distributed domain.
const DenseDom: domain(2) dmapped Block(boundingBox=Space) = Space;

// Declare a sparse subdomain.
// Since DenseDom is Block-distributed, SparseDom will be as well.
var SparseDom: sparse subdomain(DenseDom);

// Add some elements to the sparse subdomain.
// SparseDom.bulkAdd is another way to do this that allows more control.
SparseDom += [ (1,2), (3,6), (5,4), (7,8) ];

// Declare a sparse array.
// This array is also Block-distributed.
var A: [SparseDom] int;

A = 1;

writeln( "A[(1, 1)] = ", A[1,1]);
for (ij,x) in zip(SparseDom, A) {
writeln( "A[", ij, "] = ", x, " on locale ", x.locale);
}

// Results in this output when run on 4 locales:
// A[(1, 1)] = 0
// A[(1, 2)] = 1 on locale LOCALE0
// A[(3, 6)] = 1 on locale LOCALE1
// A[(5, 4)] = 1 on locale LOCALE2
// A[(7, 8)] = 1 on locale LOCALE3
```