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H A Dk_cosf.cdiff 152951 Wed Nov 30 11:51:17 MST 2005 bde Rearranged the polynomial evaluation to reduce dependencies, as in
k_tanf.c but with different details.

The polynomial is odd with degree 13 for tanf() and odd with degree
9 for sinf(), so the details are not very different for sinf() -- the
term with the x**11 and x**13 coefficients goes awaym and (mysteriously)
it helps to do the evaluation of w = z*z early although moving it later
was a key optimization for tanf(). The details are different but simpler
for cosf() because the polynomial is even and of lower degree.

On Athlons, for uniformly distributed args in [-2pi, 2pi], this gives
an optimization of about 4 cycles (10%) in most cases (13% for sinf()
on AXP, but 0% for cosf() with gcc-3.3 -O1 on AXP). The best case
(sinf() with gcc-3.4 -O1 -fcaller-saves on A64) now takes 33-39 cycles
(was 37-45 cycles). Hardware sinf takes 74-129 cycles. Despite
being fine tuned for Athlons, the optimization is even larger on
some other arches (about 15% on ia64 (pluto2) and 20% on alpha (beast)
with gcc -O2 -fomit-frame-pointer).
H A Dk_sinf.cdiff 152951 Wed Nov 30 11:51:17 MST 2005 bde Rearranged the polynomial evaluation to reduce dependencies, as in
k_tanf.c but with different details.

The polynomial is odd with degree 13 for tanf() and odd with degree
9 for sinf(), so the details are not very different for sinf() -- the
term with the x**11 and x**13 coefficients goes awaym and (mysteriously)
it helps to do the evaluation of w = z*z early although moving it later
was a key optimization for tanf(). The details are different but simpler
for cosf() because the polynomial is even and of lower degree.

On Athlons, for uniformly distributed args in [-2pi, 2pi], this gives
an optimization of about 4 cycles (10%) in most cases (13% for sinf()
on AXP, but 0% for cosf() with gcc-3.3 -O1 on AXP). The best case
(sinf() with gcc-3.4 -O1 -fcaller-saves on A64) now takes 33-39 cycles
(was 37-45 cycles). Hardware sinf takes 74-129 cycles. Despite
being fine tuned for Athlons, the optimization is even larger on
some other arches (about 15% on ia64 (pluto2) and 20% on alpha (beast)
with gcc -O2 -fomit-frame-pointer).

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