[EMAIL PROTECTED] wrote:
I just (re-)discovered these tables giving maximum known errors in some
libm functions when extended precision is enabled:
http://people.inf.ethz.ch/gonnet/FPAccuracy/linux/summary.html
and when the precision of the mantissa is set to 53 bits (double
precision):
http://people.inf.ethz.ch/gonnet/FPAccuracy/linux64/summary.html
This is from 2002, and indeed, some of the errors in double-precision
results are hundreds or thousands of times bigger when the precision is
set to 53 bits.
This isn't very helpful. I can't find an indication of whose libm is
being tested, it appears to be an unspecified non-standard version of
gcc, and a lot of digging would be needed to find out what the tests
are. It makes no sense at all for sqrt() to break down with change in
precision mode.
Extended precision typically gives a significant improvement in accuracy
of complex math functions, as shown in the Celefunt suite from TOMS.
The functions shown, if properly coded for SSE2, should be capable of
giving good results, independent of x87 precision mode. I understand
there is continuing academic research.
Arguments have been going on for some time on whether to accept
approximate SSE2 math libraries. I personally would not like to see new
libraries without some requirement for readable C source and testing.
I agree that it would be bad to set 53-bit mode blindly for a library
which expects 64-bit mode, but it seems a serious weakness if such a
library doesn't take care of precision mode itself.
The whole precision mode issue seems somewhat moot, now that years have
passed since the last CPUs were made which do not support SSE2, or the
equivalent in other CPU families.
