Thank you all. Your examples are really surprising to me.
On Thu, Nov 7, 2013 at 6:20 PM, Todd O'Bryan <toddobr...@gmail.com> wrote: > I just found a lovely Java expression to emphasize the inexactness of > doubles to my AP students. The problem--which I think is from > HtDP/1e--is to find the value of a bag of coins given the number of > pennies, nickels, dimes, and quarters. In BlueJ's code pad (or similar > in DrJava, jGrasp, etc.) > > > 0.01 + 0.05 + 0.10 + 0.25 > 0.410000000000000000003 > > (my number of zeroes may be off) > > As one of my students said--"You can do that in your head. What's the > computer's problem?" > > Todd > > On Wed, Nov 6, 2013 at 1:30 PM, Neil Toronto <neil.toro...@gmail.com> > wrote: > > On 11/06/2013 09:24 AM, Matthias Felleisen wrote: > >> > >> > >> On Nov 6, 2013, at 7:13 AM, Ben Duan <yfe...@gmail.com> wrote: > >> > >>> Thank you, Jens. I didn't know that the inexactness of floating point > >>> numbers could make such a big difference. > >> > >> > >> > >> From HtDP/1e: > >> > >> (define JANUS > >> (list #i31 > >> #i2e+34 > >> #i-1.2345678901235e+80 > >> #i2749 > >> #i-2939234 > >> #i-2e+33 > >> #i3.2e+270 > >> #i17 > >> #i-2.4e+270 > >> #i4.2344294738446e+170 > >> #i1 > >> #i-8e+269 > >> #i0 > >> #i99)) > >> > >> > >> > >> ;; [List-of Number] -> Number > >> ;; add numbers from left to right > >> (check-expect (sumlr '(1 2 3)) 6) > >> (define (sumlr l) > >> (foldl + 0 l)) > >> > >> ;; [List-of Number] -> Number > >> ;; add numbers from right to left > >> (check-expect (sumrl '(1 2 3)) 6) > >> (define (sumrl l) (foldr + 0 l)) > >> > >> Then apply the two functions to JANUS. Enjoy -- Matthias > > > > > > Nice example! > > > > You could also (require math) and apply its `sum' or `flsum' to JANUS. > Then > > *really* enjoy. :D > > > >> (sumlr JANUS) > > 99.0 > > > >> (sumrl JANUS) > > -1.2345678901235e+80 > > > >> (sum JANUS) > > 4.2344294738446e+170 > > > >> (exact->inexact (sumlr (map inexact->exact JANUS))) > > 4.2344294738446e+170 > > > > On my computer, using `sum' is about 20x faster than converting JANUS to > > exact numbers. > > > > You can also sort by absolute value before summing, which is a little > faster > > still but loses some precision. Do not trust Teh Internets on this one. > > Popular Q-and-A sites say to sort ascending, which makes intuitive sense: > > adding a big number to two small numbers in turn might do nothing, but > > adding a big number to their *sum* might result in something larger. > > > >> (expt 2 53.0) > > 9007199254740992.0 > > > >> (sumlr (list (expt 2 53.0) 1.0 1.0)) > > 9007199254740992.0 > > > >> (sumlr (list 1.0 1.0 (expt 2 53.0))) > > 9007199254740994.0 > > > > But JANUS shows that sorting ascending doesn't work when summing huge > > numbers with alternating signs: > > > >> (sumlr (sort JANUS (λ (x y) (< (abs x) (abs y))))) > > 0.0 > > > >> (sumlr (sort JANUS (λ (x y) (> (abs x) (abs y))))) > > 4.2344294738446e+170 > > > > All the research papers on summation by sorting sort descending, > contrary to > > the wisdom of Teh Internets. So either do that, or use `sum' or `flsum' > when > > you want an accurate sum of flonums. > > > > Neil ⊥ > > > > > > ____________________ > > Racket Users list: > > http://lists.racket-lang.org/users > > ____________________ > Racket Users list: > http://lists.racket-lang.org/users >
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