On 09/16/2012 04:10 PM, Matthias Felleisen wrote:
Suppose we had started Racket long ago and maintained it until now. Then we'd
be looking at 8bit, 16, 32, and 64 precision. In some N years from now, we may
need 128. (Actually there were machines in the past that did, but never mind.)
Could we separate precision and type into separate dimensions so that we could
state types like this:
∀ p : precision. FP[p] -> FP[p]
where we see FP as a type constructor that consumes a precision value to
generate the right kind of type. This might be a dependent type but it could be
a useful one. Of course, it isn't really a parametric form of polymorphism as
Neil's functions show (and better still Vincent's rewrites).
80-bit, and then 128-bit flonums are inevitable.
After TR has type classes or something like them, this would work really
well. The C++ Boost libraries use templates to achieve something
similar. Functions with an FPU implementation (sin, exp, etc.) just
dispatch to the proper bare-metal function. Functions without an FPU
implementation (gamma, erf, etc.) also dispatch depending on precision,
but can share implementation details when the algorithms are similar.
(Example: the gamma function uses a different Lanczos polynomial for
each precision, but always uses it in the same way.) Compositions of
either kind are fully polymorphic.
Neil ⊥
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