On Oct 14, 2010, at 12:07 PM, cej38 wrote:
> I am kinda sorry that I started this whole thing. I don't need
> another lesson in limits. The simple fact of the matter is that, in
> my code, I run into a place where I have a comparison (= some-value
> (some-function some-data)), the function, data, and value can change.
> In a use case that I am interested in, I run into the problem stated,
>
> user=> (= 0.0001 (- 12.305 12.3049))
> false
>
> I am OK with replacing the = function with something like float=
> discussed above, but whatever I change it two needs to work. If
> anyone has found a way, that reliably works, please post it here.
> Further, <, >, <=, and >= would also be appreciated. Thank you.
>
>
If you define 2 of them, then you get the rest for free. We already have float=:
(defn float=
([x y] (float= x y 0.00001))
([x y epsilon]
(let [scale (if (or (zero? x) (zero? y)) 1 (Math/abs x))]
(<= (Math/abs (- x y)) (* scale epsilon)))) )
If x < y, then in our case x should be more than epsilon below y:
(defn float<
([x y] (float< x y 0.00001))
([x y epsilon]
(let [scale (if (or (zero? x) (zero? y)) 1 (Math/abs x))]
(< x (- y (* scale epsilon)))) ))
(defn float<=
([x y] (or (float< x y) (float= x y)))
([x y epsilon] (or (float< x y epsilon) (float= x y epsilon))))
(defn float>
([x y] (not (float<= x y)))
([x y epsilon] (not (float<= x y epsilon))))
(defn float>=
([x y] (or (float> x y) (float= x y)))
([x y epsilon] (or (float> x y epsilon) (float= x y epsilon))))
Then you determine how strict epsilon needs to be:
(float< 12.3049 12.305) => false
(float< 12.3049 12.305 1e-6) => true
(float<= 12.305 12.3049) => true
(float<= 12.305 12.3049 1e-6) => false
(float> 12.305 12.3049 1e-6) => true
Have all good days,
David Sletten
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