The Fortress Language Specification - CiteSeerX

a new coercion in a subexpression—but this is exactly the desired effect. Once this is done, then the subexpressions
of the functional call are processed recursively.
This process is general enough not only to provide for widening floating-point precision, but to handle two other
cases of interest as well: widening point computations to interval computations, and widening computations involving
aggregate data structures whose components are widenable. For example, in d(v × w) suppose that d is of type R64
and v and w are 3-vectors with components of type R32; this strategy is capable of promoting v and w to 3-vectors
with components of type R64 and then performing all computations with R64 precision.
Let’s go through the example of c + a · b in detail. The relevant declarations might look something like this:
trait R32
. . .
end
trait R64
widening coercion (x : R32) = . . .
. . .
end
opr · (l: R32, r: R32): R32 = . . . (∗ 1 ∗)
opr · (l: R64, r: R64): R64 = . . . (∗ 2 ∗)
opr +(l: R32, r: R32): R32 = . . .(∗ 3 ∗)
opr +(l: R64, r: R64): R64 = . . .(∗ 4 ∗)
The bottom-up analysis observes that a and b are both of type R32 , and discovers that declarations 1 and 2 are
both applicable to the product, but declaration 1 would be chosen because it requires no coercion and declaration
2 would require coercion of both arguments to type R64 . The analysis then observes that c has type R64 and the
product expression has type R32 , so declaration 3 is not applicable but declaration 4 is applicable (though requiring
a coercion from R32 to R64 for its second argument).
Now the top-down widening analysis is performed. The product is a functional call that is an argument to another
functional call, and its result requires coercion, and that coercion is a widening coercion. Therefore the compiler
reconsiders the applicable declarations, which were declarations 1 and 2 . The result type of declaration 1 is not
a subtype of R64 , but the result type of declaration 2 is a subtype of R64 (in fact, it is R64 ). Declaration 2 is
the most specific among the applicable declarations with that property (in fact, in this example it’s the only one), so
declaration 2 replaces declaration 1 for the product invocation. This in turn requires a and b to be coerced from
type R32 to R64 before the product is performed.
Widening is a tricky business, best left to expert library designers. When used judiciously, it can greatly improve the
precision of numerical computations without requiring a great deal of thought on the part of the application programmer
and without cluttering up code with explicit conversions.
Future versions of this specification will include tables of coercions and widening coercions supported by the Fortress
standard libraries.
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