How to change Racket expression to Float type following Optimization Coach suggestion?

Question

I am writing a small numeric program, using Typed Racket. I want to improve its performance, and installed the Optimization Coach plugin in DrRacket. However, I am not able to follow its advice in the very first suggestion that it outputs.

The code is the following (you can see it in context here in Github):

  (define:  : Positive-Integer 20)
  (define: base : Positive-Integer 10)
  (define: N : Integer (* (+ n ) (exact-floor (/ (log base) (log 2)))))

and the Optimization Coach output is the following:

This seems simple enough, right? 2 can be changed to 2.0 and this yields an optimization (a less red color on the line), but it is base that I cannot touch without getting a TypeCheck error.

Defining or casting base as Float

  (define: base : Float 10.0)
  ;; or
  (log (cast base Float))

leads to:

❯ raco exe bellard.rkt
bellard.rkt:31:47: Type Checker: type mismatch
  expected: Real
  given: Number
  in: (/ (log base) (log 2))

How can I perform this optimization? Any help is appreciated.

Answer 1

This is a bit silly, but I found the answer to my question in the paper that presents Optimization Coach, which I had read too hastily.

Unbeknownst to the programmer, however, this code suffers from a special case in Racket’s treatment of mixed-type arithmetic. Integer-float multiplication produces a floating point number, unless the integer is 0, in which case the result is the integer 0. Thus the result of the above multiplication is a floating-point number most of the time, but not always, making floating-point specialization unsafe

I supposed this also applied to mixed-type division, and changed my code to:

(define: N : Integer (* (+ n ) (exact-floor (/ (log (exact->inexact base))
                                                (log 2.0)))))

The optimization is confirmed by the plugin with a green line.