The Fortress Language Specification - CiteSeerX

Several common mathematical operators are defined to be reduction operators in the Fortress standard libraries. These
include + , ·, ∧ , ∨ , and ∨ . If a type T extends GroupT, +, −,id (see Section 37.4 for details about the Group
trait) then reduction expressions of the form:
x −= y
are transformed into:
x += x.id − y
Note that since there are no guarantees on the order of execution of loop iterations, there are also no guarantees on the
order of reduction.
The semantics of reductions enables implementation strategies such as OpenMP [22]: A reduction variable l is assigned
l.id at the beginning of each iteration. The original variable value may be read ahead of time, resulting in the
loss of parallel updates to the variable which occur in other threads while the loop is running. Note that because this
implementation strategy does not read reduction variables in the loop body, the actual implementation of reduction
may vary substantially from the execution.
In the following example, sum is a reduction variable:
arraySumnat x(a : R64[x]) : R64 = do
sum : R64 := 0
for i ← a.indices do
sum := sum + a i
end
sum
end
13.16 Ranges
Syntax:
Range ::= [Expr] : [Expr][ : [Expr]]
| Expr # Expr
A range expression is used to create a special kind of Generator for a set of integers, called a Range, useful for
indexing an array or controlling a for loop. Generators in general are discussed further in Section 13.17.
An explicit range is self-contained and completely describes a set of integers. Assume that a, b, and c are expressions
that produce integer values.
• The range a :b is the set of n = max(0, b − a + 1) integers {a, a + 1, a + 2, . . .,b − 2, b − 1, b}. This is a
nonstrided range. If a and b are both static expressions (described in Section 13.27), then it is a static range of
type StaticRangea, n, 1 and therefore also a range of static size) of type RangeOfStaticSizen .
• The range a :b:c is the set of n = max ( 0, ⌊ ⌋) ⌊
b−a+c
c integers {a, a + c, a + 2c, . . .,a + b−a
⌋
c c}, unless c is
zero, in which case it throws an exception. (If c is a static expression, then it is a static error if c is zero.) This is
a strided range. If a , b , and c are all static expressions, then it is a static range of type StaticRangea, n, c
and therefore also a range of static size) of type RangeOfStaticSizen .
• The range a #n is the set of n integers {a, a+1, a+2, . . ., a+n−3, a+n−2, a+n−1}, unless n is negative,
in which case it throws an exception. (If n is a static expression, then it is a static error if n is negative.) This is
a nonstrided range. If a and n are both static expressions, then it is a static range of type StaticRangea, n, 1
If b is a static expression, then it is a range of static size of type RangeOfStaticSizen , even if a is not a
static expression.
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