If you limit your operations to positive integers, all you need are the three primitive operations inc, dec and zero?. Then you can build up the other operations pretty much as you did.
However, bit shifts are far from the only way to build these three primitives. For example: (def zero? empty?) (def inc vector) (def dec first) Should work too, assuming you "seed" with an empty collection as a zero. I'm not guaranteeing any kind of perfomance or the ability to represent large numbers with this scheme and the current clojure implementation. On Monday, 9 December 2013, Jim - FooBar(); wrote: > Hi all, > > A very popular interview question is to try implement all arithemtic > operations for integers without using all the usual suspects. After > thinking for a while I concluded that I only really need inc/dec in order > to implement everything else. And the good news is that one can easily > implement inc/dec using bit-shifts like so: > > (ns interview.arithmetic > (:refer-clojure :exclude [- * / + inc dec even? odd?])) > > > (defn even? [x] > (== 0 (bit-and x 1))) > > (defn odd? [x] > (== 1 (bit-and x 1))) > > (defn- halve-int [x] > (bit-shift-right x 1)) > > (defn- double-int [x] > (bit-shift-left x 1)) > > (defn inc [x] > (cond > (even? x) (bit-xor x 1) > (== -1 x) 0 > :else > (-> x > halve-int > inc > double-int))) > > (defn dec [x] > (if (odd? x) (bit-xor x 1) > (-> x > bit-not > inc > bit-not))) > > At this point, having this I can implement all arithmetic operations on > integers by combining 'iterate' + take/take-while. For example here is +: > > (defn + > ([] 0) > ([x] x) > ([x y] > (let [iter (if (neg? y) dec inc)] > (->> x > (iterate iter) > (take (inc (Math/abs y))) > last))) > ([x y & more] > (reduce + x (cons y more)))) > > The same pattern applies for [- * /]. My question is, can anyone see a > better way of doing this? It seems pretty elegant to me but I'd like to see > what other people think... > > many thanks :) > > Jim > > ps: division is indeed a bit trickier than the rest due to > positive/negative signs. Not really hard though... > > -- > -- > You received this message because you are subscribed to the Google > Groups "Clojure" group. > To post to this group, send email to clojure@googlegroups.com > Note that posts from new members are moderated - please be patient with > your first post. > To unsubscribe from this group, send email to > clojure+unsubscr...@googlegroups.com > For more options, visit this group at > http://groups.google.com/group/clojure?hl=en > --- You received this message because you are subscribed to the Google > Groups "Clojure" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to clojure+unsubscr...@googlegroups.com. > For more options, visit https://groups.google.com/groups/opt_out. > -- -- You received this message because you are subscribed to the Google Groups "Clojure" group. To post to this group, send email to clojure@googlegroups.com Note that posts from new members are moderated - please be patient with your first post. To unsubscribe from this group, send email to clojure+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/clojure?hl=en --- You received this message because you are subscribed to the Google Groups "Clojure" group. To unsubscribe from this group and stop receiving emails from it, send an email to clojure+unsubscr...@googlegroups.com. For more options, visit https://groups.google.com/groups/opt_out.
