Did you try it? It seems to me that this just makes things worse: round=: [ * [: <. 0.5 + %~ round 0.5 + 50.4 2e10 1e30 _ |NaN error: round
Thanks, -- Raul On Thu, Jan 14, 2016 at 4:28 PM, Kip Murray <[email protected]> wrote: > Try > > round > [ * [: <. 0.5 + %~ > > which I found in j602. > > --Kip Murray > > On Thu, Jan 14, 2016 at 1:56 PM, Marshall Lochbaum <[email protected]> > wrote: > >> Here's something I spent far too long on, and consequently thought was >> worth sharing. I can turn it into an essay on the J wiki if people want >> that. >> >> Recently I ran into the problem of rounding a J floating point number to >> an integer, and forcing the result to have integer type. This seems like >> a simple task: using a standard rounding function, we have >> 0.5 <.@:+ 2.3 5.1 7.6 3.9 >> 2 5 8 4 >> But with numbers that are too large, the result still contains >> floating-point numbers, and has type 8 (floating point) rather than 4 >> (integer). >> 0.5 <.@:+ _1e50 2e30 _ >> _1e50 2e30 _ >> 3!:0 ]0.5 <.@:+ _1e50 2e30 _ >> 8 >> When applied to a float, (<.) applies the C floor function, which yields >> another float, and than casts the results to integers if all of them are >> exactly representable as integers. They're not here, so they are left as >> floating-point numbers. >> >> To give a more accurate problem statement, I want the 64-bit signed >> integer which is closest to the function input. Thus numbers above the >> maximum representable integer should round to that integer, and likewise >> for numbers below the minimum representable integer. We define these two >> bounds now. >> MAX =: ->: MIN =: _2 <.@^ 63 >> Note that since MAX is one less than 2^63, trying to take (2<.@^63) >> would give us a float, and subtracting one would still leave us with a >> floating point number, which is not actually equal to MAX since (>:MAX) >> is representable as a float, while nearby integers are not. MIN on the >> other hand is safely computed as an exponent. Note the negative base, >> which works because 63 is odd. >> >> With these bounds, our problem should be easy: clamp to the integer >> range, then use (<.). >> ([: <. MIN>.MAX<.]) 0.5 + __ _1e30 _1e10 _100.3 >> _9223372036854775808 _9223372036854775808 _10000000000 _100 >> So far, so good... >> ([: <. MIN>.MAX<.]) 0.5 + 50.4 2e10 1e30 _ >> 50 2e10 9.22337e18 9.22337e18 >> Oops. What happened? >> MAX <. _ >> 9.22337e18 >> Since one of the arguments is a float, (<.) casts both to floats, and >> takes the minimum. But the closest floating-point number to MAX is >> (MAX+1), and that number's floor (MAX+1) isn't representable as an >> integer--it's one too big. We didn't have this problem with MIN, since >> it is exactly a negative power of two. >> <. MAX+1 >> 9.22337e18 >> >> We'll make a test case that contains numbers close to both bounds. I've >> included the addition of 0.5 in t so I can focus on the floor function >> from now on. The type of our result is a float, so we failed. >> t =. 0.5 + __,_,~ (MIN,0,MAX) +/(,@:) i:1e5 >> 3!:0 ([: <. MIN>.MAX<.]) t >> 8 >> >> We can fix the problem by using exact integers, but it's extremely slow. >> However, it serves as a good answer key. The ("0) is there for a >> reason--otherwise the big array of exact integers tends to flood RAM. >> fl_e =: (MIN>.MAX<.<.)&.:x:"0 NB. exact floor >> 3!:0 key =. fl_e t >> 4 >> 10 (6!:2) 'fl_e t' >> 3.62018 >> >> If we use a number small enough that its floating-point representation >> is equal to a 64-bit integer, then we can force our answer to be a >> float, but it's not correct since the results are sometimes too small. >> If that doesn't matter and speed is critical, this is the right method >> to use. >> MAX1 =. MAX - 512 >> fl_f =: [: <. MIN>.MAX1<.] NB. fast floor >> 3!:0 fl_f t >> 4 >> key -: fl_f t >> 0 >> 10 (6!:2) 'fl_f t' >> 0.0179205 >> >> Finally, my solution. It's not particularly elegant, but it is correct >> and has good performance. We reduce all the values larger than MAX to >> zero, then clamp on the minimum side and take the floor. For the values >> that we removed, we add MAX back in. The comparison (<:&MAX) is only >> computed once to save a little time. >> fl =: ((MAX*-.@]) + [: <. MIN>.*) <:&MAX >> key -: fl t >> 1 >> 10 (6!:2) 'fl t' >> 0.0426181 >> It's critical to use (<:) rather than (<) to test whether numbers are >> acceptable even though it fails MAX, which wouldn't break (<.). That's >> because comparisons cast their arguments to floats before comparing, so >> MAX < MAX+1 >> 0 >> >> Maybe there's a quicker solution to be found. The following rounds >> towards zero quickly by negating all the positive numbers, and restoring >> their signs later. However, adding in the cases to make it equal to (<.) >> on small numbers removes its advantage. >> fl_o =: (] * MIN <.@:>. *) -@:* NB. floor towards zero >> fl_o _4.6 _3 _2.8 _1.2 3.4 5.8 9 >> _5 _3 _3 _2 4 6 9 >> 10 (6!:2) 'fl_o t' >> 0.0324293 >> >> Any takers? >> >> Marshall >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
