30 Jan
2011
30 Jan
'11
2:29 p.m.
Excerpts from Peter Nelson's message of 2011-01-29 13:47:07 +0100:
On Sat, 2011-01-29 at 12:07 +0100, Philipp Überbacher
wrote:
Is it really surprising (for the non-optimised variant)? Your variant
uses one less variable and assignment. That this isn't optimised away
completely with -O3 does surprise me too.
Excerpts from fons's message of 2011-01-28
16:11:52 +0100:
log2() suffers from the same problem? I somewhat dislike the idea of
adding a constant.
Well, now I'm just being pedantic :-), but as a quick test using rdtsc
(i.e. profiling to be taken with a grain of salt):
1: log(x)/log(2)
2: (1 << k) < x
3: m < x & m <<= 1
This is 1000 iterations; cycling through x of 512, 1024, 2048, 4096 (to
prevent the compiler optimizing log(x)/log(2) to a single call
throughout the whole test). The fourth line is the sum of the iterator
in each loop.
./a.out (unoptimized)
1 3132000 cycles
2 261468 cycles
3 285273 cycles
1 50500, 2 50500, 3 50500
./a.out (-O3)
1 2598345 cycles
2 170055 cycles
3 173673 cycles
1 50500, 2 50500, 3 50500
I must admit, I'm surprised that fons way shows slightly slower in my
test! On Fri, Jan 28, 2011 at 02:02:36PM +0100, Philipp
Überbacher wrote:
Took me a while to figure out that libm is part of glibc :)
Good to know that those functions are available on probably pretty much
all linux systems.
rant_begin
Why can't log mean the same thing everywhere? Why does it need to be
base e here and base 10 there? Why is there no consistency?
And why is there no proper logarithmus dualis function? Because you
can simply do log(n)/log(2)? We've just seen how well this works.
How about:
log() - base 10
ln() - base e - logarithmus naturalis
ld() - base 2 - logarithmus dualis
rant_end
Libm has log(), log10, and log2(). The next
obvious question is: Does the inaccuracy reliably result in
values bigger than 11?
No.
If the input is a power of two, and you expect an integer as
a result, just do
k = (int)(log2(x) + 1e-6) or
k = (int)(log(x)/log(2) + 1e-6)
or
int m, k;
for (k = 0, m = 1; m < x; k++, m <<= 1);
which will round up if x is not a power of 2.
Neat. I thought about it myself yesterday but my ideas weren't exactly
brilliant. One idea was to divide by 2, the other to use a small
lookup table for powers of 2. I don't really know about efficiency, but
I guess bit shifting is as efficient as it gets?
Anyway, it's a neat way to avoid the problem and the rounding properties
of mult/div in case of not power of 2 could be useful as well. As an aside, here's the result with (-O3
-ffast-math)
./a.out
1 150894 cycles,
2 169983 cycles,
3 158850 cycles,
1 47750, 2 50500, 3 50500
Yeah, faster, but wrong :-)
Peter.
After a brief look at man gcc -ffast-math doesn't seem like a very good
idea to use it in general, so no surprise it's not part of -O3 or
something.
Quite interesting stuff, thanks Peter.