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Re: Performance analysis of Polyhedron/gas_dyn
Geert Bosch wrote:
On Apr 27, 2007, at 06:12, Janne Blomqvist wrote:
I agree it can be an issue, but OTOH people who care about precision
probably 1. avoid -ffast-math 2. use double precision (where these
reciprocal instrs are not available). Intel calls it -no-prec-div, but
it's enabled for the "-fast" catch-all option.
No, using only 12 bits of precision is just ridiculous and should
not be included in -ffast-math. You should always use a Newton-Rhapson
step after getting the 12-bit approximation.
Yes, I realize that.
When done correctly
this doubles the precision and gets you just about the 24 bits of
precision needed for float. Reciprocal approximations are meant
to be used that way, and it's no accident the lookup provides
exactly half the bits needed. For double precision you just do
two more iterations, which is why there is no need for double
precision variants of these instructions.
However, I didn't realize so few iterations were required to achieve
(almost) full precision. That's pretty nice.
The cost for the extra step is small, and you get good results.
There are many variations possible, and using fused-multiply add
it's even possible to get correctly rounded results at low cost.
I truly doubt that any of the compilers you mention use these
instructions without NR iteration to get required precision.
I guess so. I haven't checked the others, but Intel does indeed do a
single NR step. However, if I change the subroutine in question to
double precision, it uses divpd and sqrtpd instead of two NR iterations.
According to the benchmarks I linked to in PR 31723, it could actually
be faster to use the reciprocal + 2 NR iters for double precision,
though in my own testing it turned out to be a wash.
--
Janne Blomqvist