On 02/09/2014 12:43, peter dalgaard wrote:
Impressive. Never ceases to amaze me what computers can do these days. ;-)
It's even more impressive given that we have
static double logbase(double x, double base)
{
#ifdef HAVE_LOG10
if(base == 10) return x > 0 ? log10(x) : x < 0 ? R_NaN : R_NegInf;
#endif
#ifdef HAVE_LOG2
if(base == 2) return x > 0 ? log2(x) : x < 0 ? R_NaN : R_NegInf;
#endif
return R_log(x) / R_log(base);
}
which, except possibly for base-10 and base-2, would seem to be quite hard to
convince to return anything other than 1 if x == base....
I suspect PD knows (or has known) why, but for the sake of those who are
not much bitten by ix86 compilers ....
It's the curse of extended-precision arithmetic (and not enough
registers). It does
compute in an FPU register, then store z1 = R_log(x)
compute z2 = R_log(base) in the FPU
load z1 to an FPU register.
compute z1/z2
(at least at -O2 with the version of gcc whose assembler output I looked
at). So z1 is has a 64-bit mantissa and z2 a 53-bit one.
x86_64 has more registers, and so avoids the store. This can be
circumvented on i686 by compiling with -msse2, which for some reason
Linux distros do not make the default.
floor(log2(x)/3) is more reliable (and this is the underlying reason why
we have log10 and log2).
-pd
On 02 Sep 2014, at 03:27 , Ben Bolker <bbol...@gmail.com> wrote:
log(8, base=8L)-1
log(8, base=8)-1
logvals <- setNames(log(2:25,base=2:25)-1,2:25)
logvals[logvals!=0] ## 5,8,14,18,19,25 all == .Machine$double.eps/2
--
Brian D. Ripley, rip...@stats.ox.ac.uk
Emeritus Professor of Applied Statistics, University of Oxford
1 South Parks Road, Oxford OX1 3TG, UK
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