# Ranges¶

View ranges.chpl on GitHub

This primer illustrates Chapel ranges and range operations.

## Range Basics¶

Ranges represent regular sequences of values, such as integers, and are typically defined in terms of a low and high bound. Range values can be specified using the `..` operator, where the low bound is specified on the left side of the `..` and the high bound is on the right. These bounds are inclusive for ranges created with `..`.

```const n = 5,
lo = -3,
hi = 3;
writeln("Basic ranges");
const r = 1..10,    // 1, 2, 3, ..., 10
r2 = 0..n,    // 0, 1, 2, ..., n
r3 = lo..hi;  // -3, -2, -1, ..., 3
writeRange(r);
writeRange(r2);
writeRange(r3);
writeln();
```

Ranges can also be defined using an open-interval form using the `..<` operator, causing the upper bound to be excluded from the values represented by this range. For example, the range `3..<10` is equivalent to `3..9`. This form is particularly useful for 0-based indexing, to avoid bounds like `n-1`.

```writeln("Open interval ranges");
const rOpen = 1..<10,  // 1, 2, 3, ..., 9
rOpen2 = 0..<n;  // 0, 1, 2, ..., n-1
writeRange(rOpen);
writeRange(rOpen2);
writeln();
```

Note that whenever a range’s low bound exceeds its high bound, the range is considered to be empty.

```writeln("Empty ranges");
const empty1 = 1..0,
empty2 = 0..-1,
empty3 = 10..1;
writeRange(empty1);
writeRange(empty2);
writeRange(empty3);
writeln();
```

To create a range representing a decreasing series of values, the `by` operator can be used with a negative stride. As a simple example, the following range represents the integers counting from 10 down to 1.

```writeln("Decreasing range");
const countDown = 1..10 by -1;  // 10, 9, 8, ..., 1
writeRange(countDown);
writeln();
```

See the Range Operators section below for more information about strided ranges and the `by` operator.

## Uses of Ranges¶

Ranges are a basic building block for iteration. The following for-loop iterates over the sequence represented by `r`, computing the sum of the values in the sequence.

```var sum = 0;
for i in 1..10 do       // compute 1 + 2 + 3 + ... + 10
sum += i;
writeln("The sum of the values in '1..10' is ", sum);
writeln();
```

Ranges can also drive parallel loop forms such as forall and coforall loops.

Ranges also serve as the building block for rectangular domains and arrays. Here we use ranges to declare a 2D 10x10 domain and an array over it.

```writeln("Domains and arrays");
const D = {1..10, 1..10};  // could also use '= {r, r};'
var A: [D] real;           // a 10x10 array of real floating point values
writeln("D = ", D);
writeln("Array A");
writeln(A);
writeln();
```

Arrays can also be declared using ranges directly, which effectively creates an anonymous domain for the array:

```var A1: [1..n] int,
A2: [1..n, 1..n] string;
```

Ranges can be used in general contexts that expect an iterable collection of values, such as reductions:

```sum = + reduce r;  // compute 1 + 2 + 3 + ... + 10
writeln("The sum of the values in ", r, ", computed by reduce, is also ", sum);
```

Or whole-array operations:

```A1 = r;      // assign the elements of A1 their corresponding values of r
writeln(A1);
writeln();
```

## Variations on Basic Ranges¶

Ranges can be unbounded on one or both sides, when the respective bound is omitted. For example, a range without a high bound represents values greater than or equal to the low bound.

```writeln("Unbounded ranges");
writeRange(1..);   // 1, 2, 3, ...
writeRange(..5);   // ..., 3, 4, 5
writeRange(..);    // ...
writeln();
```

Loops may iterate over an unbounded range as long as it has a well-defined first value to start from. When an unbounded range of integers is zipped with another iterator expression, its size automatically conforms to the required size.

```writeln("Iterating over zip(312..315, 1..) generates");
for (i, j) in zip(312..315, 1..) {
write(" ", (i, j));
}
writeln();
writeln();
```

Ranges can also be defined over boolean values and enumerated types. In the case of enumerations, the range’s sequence of values is based on the declaration order of the enum’s constants rather than their (optional) numerical values.

```writeln("Ranges over bools and enums:");
enum dir {north, south, east, west};
enum color {red=4, orange=2, yellow=1, green=3, blue=6, indigo=7, violet=5};
const boolRange = false..true,                 // false, true
enumRange = dir.north..dir.west,         // north, south, east, west
colorRange = color.orange..color.green;  // orange, yellow, green
writeRange(boolRange);
writeRange(enumRange);
writeRange(colorRange);
writeln();
```

For boolean and enum ranges, the lack of a bound implies that the type’s low/high value should be used in place of the missing bound.

```writeRange(false..);         // like 'false..true'
writeRange(dir.south..);     // like 'dir.south..dir.west'
writeRange(..color.indigo by -1);  // like 'color.red..color.indigo by -1'
writeln();
```

## Range Operators¶

New ranges can be constructed from existing ones using the count, stride, and/or alignment operators: `#`, `by`, and `align`.

The count operator `#` applies an integer count, c, to a range and generates a new range representing c of the range’s values. If the count is positive, the new range will represent the first c values; if it is negative, it represents the last c values in the range. It is an error to apply a positive count of to a range with no first value (e.g., `..10`), or a negative count to a range with no last value (e.g., `1..`).

```writeln("The count operator");
const numElements = 5;
writeRange(0..#numElements);  // 0, 1, 2, 3, 4
writeRange(r # 4);            // 1, 2, 3, 4
writeRange(..5 # -3);         // 3, 4, 5
writeln();
```

The `by` operator applies a stride to a range, selecting a subsequence of its original values. If the range was already strided, the effect is multiplicative. If the stride is negative, the direction of the sequence is reversed.

```writeln("Strided ranges using the by operator");
writeRange(r by 2);       // 1, 3, 5, 7, 9
writeRange(r by 2 by 2);  // 1, 5, 9
writeRange(r by -1);      // 10, 9, 8, ..., 1
writeRange(5.. by 2);     // 5, 7, 9, 11, ...
writeln();

writeln("Examples mixing # and by");
writeRange(r by 2 # 4);    // 1, 3, 5, 7
writeRange(r # 4 by 2);    // 1, 3
writeRange(r by -2 # 4);   // 10, 8, 6, 4
writeRange(r # 4 by -2);   // 4, 2
writeRange(r by 2 # -4);   // 3, 5, 7, 9
writeRange(r # -4 by 2);   // 7, 9
writeRange(r by -2 # -4);  // 8, 6, 4, 2
writeRange(r # -4 by -2);  // 10, 8
writeln();
```

By default, a strided range’s values are aligned with its first value. Thus, for a positive stride, the values are aligned with its low bound; while for a negative stride, the values are aligned to its high bound.

```writeln("Implicit alignment set using 'by'");
writeRange(1..10 by 2);  // values are aligned with 1: 1, 3, 5, 7, 9
writeRange(1..10 by -2); // values are aligned with 10: 10, 8, 6, 4, 2
writeRange(..5 by -3);   // values are aligned with 5: 5, 2, -1, -4, ...
const rangeWithAmbiguousAlignment = 1.. by -3;  // alignment undefined
writeln();
```

The `align` operator can be used to explicitly specify the alignment of a strided range. The indices in the aligned range are all equivalent to the specified alignment modulo the stride’s absolute value. For example, alignment can be used to define sequences representing odd numbers versus even numbers.

```writeln("Range alignment and the align operator");
const oddsBetween1and10  = r by 2 align 1,  // 1, 3, 5, 7, 9
evensBetween1and10 = r by 2 align 2;  // 2, 4, 6, 8, 10
writeRange(oddsBetween1and10);
writeRange(evensBetween1and10);

const allOdds = .. by 2 align 1,
allEvens = .. by 2 align 2;
writeRange(allOdds);
writeRange(allEvens);
writeln();
```

The alignment is always taken modulo the stride, so one could also declare ‘allEvens’ using .. by 2 align 0, .. by 2 align 12, or any other even number as the alignment.

The `+` and `-` operators can be used to create a new range from an existing one, representing a shift in the range’s sequence of values.

```writeln("Operators + and -");
writeRange(r + 5);          // 6..15
writeRange(r - 3);          // -2..7
writeRange((r by 2) - 1);   // 0..9  by 2
writeRange(1 + ..5);        // ..6
writeln();
```

The `==` operator can be used to test whether two ranges are equal. Equality means they represent the same sequence of indices.

```writeln("Range equality");
writeln(r == 1..10);                               // true
writeln((1..10 by 2) == (1..9 by 2));              // true
writeln(r == (r by 2));                            // false
writeln(oddsBetween1and10 != evensBetween1and10);  // true
writeln();
```

## Range Slicing (Intersection)¶

Range slicing is when one range is indexed using another range. This computes the intersection of the two ranges values. Slicing is commutative in most respects.

```writeln("Range slicing");
writeln("A slice of ", r, " with ", 2..7);
writeRange(r[2..7]);  // 2..7
const r1 = 5..15;
writeln("A slice of ", r, " with ", r1);
writeRange(r[r1]);    // 5..10
writeln("A slice of ", r1, " with ", r, " is the same");
writeRange(r1[r]);    // 5..10
```

Computing with the odds and evens between 1 and 10 (using range slicing):

```writeRange(r[allOdds]);   // 1, 3, 5, 7, 9
writeRange(r[allEvens]);  // 2, 4, 6, 8, 10

writeln(r[allOdds] == oddsBetween1and10);    // true
writeln(r[allEvens] == evensBetween1and10);  // true
```

Either or both of the ranges in a range slicing operation can be strided and/or unbounded When the slicing range has a negative stride, the direction of the original range is reversed. As of Chapel Release 1.30, this feature requires compiling with `-snewSliceRule`. In a subsequent release this behavior will be standard and the option `-snewSliceRule` will be removed.

```const rs = 1..20 by 3;
writeln("A slice of ", rs, " with ", 1..20 by 2);
writeRange(rs[1..20 by 2]);  // 1, 7, 13, 19
writeln("A slice of ", rs, " with ", 1..20 by -2);
writeRange(rs[1..20 by -2]); // 16, 10, 4
writeln();

writeln("A slice of ", r, " with ", 5..);
writeRange(r[5..]);       // 5, 6, 7, 8, 9, 10
writeln("A slice of ", r, " with ", 5.. by 2);
writeRange(r[5.. by 2]);  // 5, 7, 9
writeln("A slice of ", 1.., " with ", ..5);
writeRange((1..)[..5]);   // 1, 2, 3, 4, 5
writeln();
```

## Range Types¶

Range types are generic with respect to three fields:

• `idxType`: The type of the range’s values (defaults to `int`)

• `bounds`: A `boundKind` value indicating which bounds the range stores (defaults to `boundKind.both`)

• `strides`: A `strideKind` value indicating what values the range’s `strides` is allowed to store (defaults to `strideKind.one`)

Like other variables, range types can be inferred by the compiler from the initializing expression for simplicity, as in the previous examples. However, they can also be specified if desired. Here are some examples that are equivalent to ones we’ve seen before:

```const rt: range(int) = 1..10,
rt2: range(int, bounds=boundKind.both, strides=strideKind.one)
= 1..10,
rte: range(color) = color.orange..color.green,
rts: range(strides=strideKind.any) = 1..10 by 2,
rtub: range(bounds=boundKind.low) = 1..;
```

More importantly, range types can be used to make a range variable more flexible than its initializer permits. For example, this range’s initializer has a unit stride, but because its type is declared with `strideKind.any`, it can later be assigned a range value with a stride.

```var rangeVar: range(int, strides=strideKind.any) = 1..10;
```

Range types are also valuable in declaring formal arguments of a procedure in which you want to leave certain aspects of the range constrained or unconstrained.

```proc acceptsNonStridedIntRangesOnly(r: range(int)) { }
proc acceptsAnyRange(r: range(?)) { }

acceptsNonStridedIntRangesOnly(1..10);
acceptsAnyRange(1..10);
acceptsAnyRange(1..10 by 2);
acceptsAnyRange(color.orange..color.green);
```

## Helper function for this primer: writeRange()¶

The procedure that has been used throughout this primer to print ranges is defined below. It adjusts to the specifics of the range.

```proc writeRange(r: range(?)) {
write("Range ", r);
if r.bounds == boundKind.both ||
((isBoolType(r.idxType) || isEnumType(r.idxType)) && r.hasFirst()) {
// The range is fully bounded, either because it is a bounded
// range or because it is unbounded but defined on bools or an
// enum, so - print its entire sequence.
write(" = ");
var first: bool = true;;
for i in r {
if !first then write(", ");
write(i);
first = false;
}
} else if r.hasFirst() {
// The range is not fully bounded, but its sequence has a starting point
// - print the first three indices.  Note that in this and the next
// case the sequence can be either increasing or decreasing.
write(" = ");
for i in r # 3 do
write(i, ", ");
write("...");
} else if r.hasLast() {
// The range is not fully bounded, but its sequence has an ending point.
// Print the last three indices.
write(" = ...");
for i in r # -3 do
write(", ", i);
} else if r.stride == 1 || r.stride == -1 {
// If we are here, the range is fully unbounded.
write(" = all integers, ",
if r.stride > 0 then "increasing" else "decreasing");
} else {
// We got a more complex range, do not elaborate.
}
writeln();
}
```