PATCH: optimized libm single precision routines: erfcf, erff, expf for x86_64.

[Dmitrieva Liubov]

Thanks for your changes.

About j: no sense to treat it as signed. Here is updated algorithm
with table of 2^(j/K) for j=[0;K-1]. Please, see new attached patch.

About the benchmark: this is just perfomance in cycles for main
interval [-87.0; 87.0].

Results:
Istanbul/Atom/Nehalem/AVX
Attached version:   51.63     97.23     31.12     25.34   (__AVX__
enabling gives 24.98 cycles on AVX.)

About stability: We used "make check". Also we used proprietary test
system that tests on many intervals with different steps, checks for
special values (from ISO C) and corner cases.

--
Liubov Dmitrieva
Intel Corporation

2012/2/22 Ulrich Drepper <drepper@gmail.com>:
> This time with attachment.
>
> On Wed, Feb 22, 2012 at 10:14, Ulrich Drepper <drepper@gmail.com> wrote:
>> On Tue, Feb 21, 2012 at 15:32, Dmitrieva Liubov
>> <liubov.dmitrieva@gmail.com> wrote:
>>> The updated attached version is significantly hand-tuned assembler code.
>>> We are looking forward to accepting and releasing this change.
>>
>> At least the changes made to the attached version should be made.
>> They are small but save another cycle or two.
>>
>> I don't see why the computation of j has to be that complicated.  6
>> bits are taken from the mantissa.  These are then interpreted as a
>> signed value.  Why?  I know it works but is there really a reason?
>>
>> If the bits are considered are unsigned that computation for the
>> access of the array DP_T as well as the computation of  n*k are
>> simpler (only AND, no shifting and subtracting).  The algo has to be
>> adapted but this should be possible.  I think nobody really paid
>> attention to that since the DP_T table was too large (it had 65
>> entries!).
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