On Mon, 12 Apr 2010 13:45:14 -0400, Jérôme M. Berger <jeber...@free.fr>
wrote:
Steven Schveighoffer wrote:
J�r�me M. Berger Wrote:
J�r�me M. Berger wrote:
OK, I found a solution that is optimal in over 99% of the cases
(99.195% to be precise), while still being fast (because it avoids
looping over the bits):
I've run my function and Andrei's on all possible min, max pairs in
0..299 without checking, just for the timing. On my computer (Athlon
X2 64 @2GHz), my function took 50s and Andrei's took 266s. The
difference should be even bigger for larger numbers.
Can I ask, what is the point of having a non-exact solution (unless you
are just doing this for fun)?
We are talking about range propagation, a function of the compiler, not
a function of the compiled program. Therefore, slower but more exact
functions should be preferred, since they only affect the compile
time. Note that you will only need to do this range propagation on
lines that "or" two values together, and something that reduces the
runtime of the compiler by 216 seconds, but only when compiling enough
code to have over 8 billion 'or' operations in it (300^4), I don't
think is really that important. Give me the exact solution that
prevents me from having to cast when the compiler can prove it, even if
the runtime of the compiler is slightly slower.
Funny you should say that given the current thread comparing the
speed of the D compiler to that of the Go compiler...
My point was simply that the amount of time saved is relative to the size
of the program being compiled. If we assume conservatively that every
other line in a program has bitwise or in it, then you are talking about a
16 billion line program, meaning the 216 seconds you save is insignificant
compared to the total compile time. My point was that your fast solution
that is inaccurate is not preferable because nobody notices the speed,
they just notice the inaccuracy.
We are talking about range propagation, a function of the compiler,
not a function of the compiled program. Since we can't get a 100%
accurate representation of the possible values anyway (even yours
might leave holes in the middle after all), then it might be better
to choose a faster, slightly less precise algorithm if the
difference is not too great. That's the difference between a
compiler and a full-fledged static code analysis an program prover.
When we're talking about the difference between O(1) and O(lgn), I'll take
accuracy over speed in my compiler any day. The solution should be 100%
accurate for the problem statement. If the problem statement is not what
we need, then we need a new problem statement :) Solving the problem
statement for 99% of values is not good enough.
Anyway, the point is moot, I have a new version of my algorithm
with 100% precision and high speed.
Yes, I'm still trying to understand how it works :)
-Steve
