# Ranges¶

A range is a first-class, constant-space representation of a regular sequence of values. These values are typically integers, though ranges over enum types are also supported. Ranges support iteration over the sequences they represent as well as operations such as counting, striding, intersection, shifting, and comparisons.

## Range Values¶

In their simplest form, ranges are represented by their low and high bounds:

1..3    // 1, 2, 3
0..n    // 0, 1, 2, 3, ..., n
lo..hi  // lo, lo+1, lo+2, ..., hi


Ranges may also be unbounded, in which case, the lower and/or upper bounds may be omitted:

1..   // 1, 2, 3, ...
..10  // .., 8, 9, 10
..    // ..., -2, -1, 0, 1, 2, ...


Ranges over enum types respect the declaration order of its values:

enum color {red=4, orange=2, yellow=1, green=3, blue=6, indigo=7, violet=5};
color.orange..color.green;   // orange, yellow, green


## Range Types¶

Range types are generic with respect to three fields:

• idxType: The type of the range’s values—must an integral or enum type (defaults to int)
• boundedType: A BoundedRangeType value indicating which bounds the range stores (defaults to bounded)
• stridable: A boolean indicating whether or not the range can be strided (defaults to false)

The following code shows range variables declared with specified type signatures:

var r1: range = 1..10;
var r2: range(int(8)) = 1..myInt8;
var r3: range(color) = color.green..color.blue;
var r4: range(stridable=true) = 1..10 by 2;
var r5: range(boundedType=BoundedRangeType.boundedNone) = ..;


Like other variables, these types can be inferred by the compiler from the initializing expressions for simplicity:

var r1 = 1..10;
var r2 = 1..myInt8;
var r3 = color.green..color.blue;
var r4 = 1..10 by 2;
var r5 = ..;


## Range Operators¶

New ranges can be constructed from existing ones using the counting, striding, and/or alignment operators, #, by, and align:

0..#10              // 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
0..10 by 2          // 0, 2, 4, 6, 8, 10
0..10 by 2 align 1  // 1, 3, 5, 7, 9
0.. by 2 # 10       // 0, 2, 4, 6, 8, 10, 12, 14, 16, 18


## Iteration over ranges¶

Ranges can be used as the iterable expression in for, forall, and coforall loops.

for i in 1..10 { ... f(i) ... }
forall i in 1..1000 { ... f(i) ... }
coforall i in 0..#numTasks { ... f(i) ... }


When ranges that are not fully bounded are zipped with another iterator, the other iterator is used to determine an ending point.

// (i, j) will take the values: (1, 7), (2, 8), (3, 9), (4, 10)
for (i, j) in zip(1..4, 7..) { ... }

// (i, j) will take the values: (1, 10), (2, 9), (3, 8), (4, 7)
for (i,j) in zip(1..4, ..10 by -1) { ... }


## Range Intersection¶

A range can be intersected with another range to form a new range representing the intersection of the two ranges by slicing one range with the other.

(1..10)[3..8] // 3..8
(0..20)[1..20 by 2] // 1..20 by 2
(1..10)[5..] // 5..10
(1..10)[..5] // 1..5


## Range Shifting¶

A range can be shifted by an integer using the + and - operators.

(1..10) + 5 // 6..15
(1..10) - 3 // -2..7
(1..) + 1 // 2..
(..10) + 1 // ..11


## Range Comparisons¶

Ranges can be compared for equality using the == and != operators.

1..10 == 1..10 // true
1.. == 1.. // true
1..10 != (1..10 by 2) // true

enum BoundedRangeType { bounded, boundedLow, boundedHigh, boundedNone }

The BoundedRangeType enum is used to specify the types of bounds a range is required to have.

• bounded - The range has finite low and high bounds.
• boundedLow - The range starts at a given low bound, but conceptually goes up to infinity.
• boundedHigh - The range conceptually starts at negative infinity and ends at a given high bound.
• boundedNone - The range conceptually runs from negative infinity to infinity.
proc range.intIdxType type

The idxType as represented by an integer type. When idxType is an enum type, this evaluates to int. Otherwise, it evaluates to idxType.

proc isRangeType(type t) param

Return true if argument t is a range type, false otherwise

proc isBoundedRange(r: range(?)) param

Return true if argument r is a fully bounded range, false otherwise

proc range.hasLowBound() param

Return true if this range has a low bound, false otherwise

proc range.hasHighBound() param

Returns true if this range has a high bound, false otherwise

proc range.stride

Returns the stride of the range

proc range.alignment

Returns the alignment of the range

proc range.aligned

Returns true if the range is aligned

proc range.first

Return the first element in the sequence the range represents

proc range.last

Return the last element in the sequence the range represents

proc range.low

Return the range’s low bound. If the range does not have a low bound the behavior is undefined.

proc range.high

Return the range’s high bound. If the range does not have a high bound the behavior is undefined.

proc range.alignedLow: idxType

Returns the range’s aligned low bound. If the aligned low bound is undefined (does not exist), the behavior is undefined.

proc range.alignedHigh: idxType

Returns the range’s aligned high bound. If the aligned high bound is undefined, the behavior is undefined.

proc range.isEmpty()

If the sequence represented by the range is empty, return true. An error is reported if the range is ambiguous.

proc range.length: intIdxType

Deprecated - please use range.size.

proc range.size: intIdxType

Returns the number of elements in this range, cast to the index type.

Note: The result is undefined if the index is signed and the low and high bounds differ by more than max(range.intIdxType ).

proc range.hasFirst() param

Return true if the range has a first index, false otherwise

proc range.hasLast() param

Return true if the range has a last index, false otherwise

proc range.isNaturallyAligned()

Returns true if this range is naturally aligned, false otherwise

proc range.isAmbiguous() param

Returns true if the range is ambiguously aligned, false otherwise

proc range.contains(ind: idxType)

Returns true if ind is in this range, false otherwise

proc range.contains(other: range(?))

Returns true if the range other is contained within this one, false otherwise

proc range.member(ind: idxType)

Deprecated - please use range.contains.

proc range.member(other: range(?))

Deprecated - please use range.contains.

proc ident(r1: range(?), r2: range(?))

Returns true if the two ranges are the same in every respect: i.e. the two ranges have the same idxType, boundedType, stridable, low, high, stride and alignment values.

proc range.boundsCheck(other: range(?e, ?b, ?s))

Returns true if other lies entirely within this range and false otherwise. Returns false if either range is ambiguously aligned.

proc range.boundsCheck(other: idxType)

Return true if other is contained in this range and false otherwise

proc range.indexOrder(ind: idxType)

If ind is a member of the range’s represented sequence, returns an integer giving the ordinal index of ind within the sequence using zero-based indexing. Otherwise, returns (-1):range.intIdxType. It is an error to invoke indexOrder if the represented sequence is not defined or the range does not have a first index.

The following calls show the order of index 4 in each of the given ranges:

(0..10).indexOrder(4) == 4
(1..10).indexOrder(4) == 3
(3..5).indexOrder(4) == 1
(0..10 by 2).indexOrder(4) == 2
(3..5 by 2).indexOrder(4) == -1

proc range.orderToIndex(ord: integral): idxType

Returns the zero-based ord-th element of this range’s represented sequence. It is an error to invoke orderToIndex if the range is not defined, or if ord is negative or greater than the range’s size. The orderToIndex procedure is the reverse of indexOrder.

Example:

0..10.orderToIndex(4) == 4
1..10.orderToIndex(3) == 4
3..5.orderToIndex(1)  == 4
0..10 by 2.orderToIndex(2) == 4

proc range.translate(offset: integral)

Return a range with elements shifted from this range by offset.

Example:

0..9.translate(1) == 1..10
0..9.translate(2) == 2..11
0..9.translate(-1) == -1..8
0..9.translate(-2) == -2..7

proc range.interior(offset: integral)

Return a range with offset elements from the interior portion of this range. If offset is positive, take elements from the high end, and if offset is negative, take elements from the low end.

Example:

0..9.interior(1)  == 9..9
0..9.interior(2)  == 8..9
0..9.interior(-1) == 0..0
0..9.interior(-2) == 0..1

proc range.exterior(offset: integral)

Return a range with offset elements from the exterior portion of this range. If offset is positive, take elements from the high end, and if offset is negative, take elements from the low end.

Example:

0..9.exterior(1)  = 10..10
0..9.exterior(2)  = 10..11
0..9.exterior(-1) = -1..-1
0..9.exterior(-2) = -2..-1

proc range.expand(offset: integral)

Return a range expanded by offset elements from each end. If offset is negative, the range will be contracted.

Example:

0..9.expand(1)  == -1..10
0..9.expand(2)  == -2..11
0..9.expand(-1) == 1..8
0..9.expand(-2) == 2..7

proc range.offset(in offset: integral)

Returns a range whose alignment is this range’s first index plus offset. If the range has no first index, a runtime error is generated.