On 02/19/2014 03:33 PM, Sam Tobin-Hochstadt wrote:
On Wed, Feb 19, 2014 at 5:02 PM, Neil Toronto <[email protected]> wrote:
(: random-natural/no-mean (-> Real Natural))
(define (random-natural/no-mean prob-zero)
(define n (exact-floor (sample (geometric-dist prob-zero))))
(define m1 (assert (expt 2 n) integer?))
(define m0 (quotient m1 2))
(max 0 (random-integer m0 m1)))
The "max 0" keeps TR from complaining that `random-integer' returns an
Integer.
These both look like places where `math` could do better here with types.
Specifically, `geometric-dist` should probably say that it produces
non-negative floats. That would fix the need for the `assert`.
Ah, of course.
Second, `random-integer` could have the type: (case-> (Natural Natural
-> Natural) (Integer Integer -> Integer)). That would fix the need
for `max`.
I hadn't thought of doing that.
When I wrote that function, the math library was taking 45% of the total
compilation time, so I had stopped considering case-> types that weren't
strictly necessary. I know TR has gotten faster in the meantime, so it
might be time to revisit making some of the types more precise.
Uh, after I finish writing my dissertation. :) I'm so close...
Finally, I don't understand why `geometric-dist` returns floats and
not integers, anyway.
The inverse CDF of any geometric distribution evaluated at 1 should be
infinity, as here:
> (inv-cdf (geometric-dist 0.5) 1)
+inf.0
My original reasoning was that I didn't want to deal with types like (U
Natural +inf.0) or ask users to deal with them. But now I realize that
it should be (U Natural Positive-Infinity):
> (inv-cdf (geometric-dist 0.5) 1)
+inf
i.e. the answer should be exact, not inexact.
Neil ⊥
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