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).

2 files changed, 13 insertions, 9 deletions

diff --git a/lib/msun/src/k_cosf.c b/lib/msun/src/k_cosf.c
index a3bf520..6a0afe9 100644
--- a/lib/msun/src/k_cosf.c
+++ b/lib/msun/src/k_cosf.c
@@ -37,9 +37,11 @@ extern inline
 float
 __kernel_cosdf(double x)
 {
-	double z,r;
+	double r, w, z;
 
-	z  = x*x;
-	r  = z*(C1+z*(C2+z*C3));
-	return (one+z*C0) + z*r;
+	/* Try to optimize for parallel evaluation as in k_tanf.c. */
+	z = x*x;
+	w = z*z;
+	r = C2+z*C3;
+	return ((one+z*C0) + w*C1) + (w*z)*r;
 }
diff --git a/lib/msun/src/k_sinf.c b/lib/msun/src/k_sinf.c
index 7009f82..79f32a1 100644
--- a/lib/msun/src/k_sinf.c
+++ b/lib/msun/src/k_sinf.c
@@ -36,10 +36,12 @@ extern inline
 float
 __kernel_sindf(double x)
 {
-	double z,r,v;
+	double r, s, w, z;
 
-	z	=  x*x;
-	v	=  z*x;
-	r	=  S2+z*(S3+z*S4);
-	return x+v*(S1+z*r);
+	/* Try to optimize for parallel evaluation as in k_tanf.c. */
+	z = x*x;
+	w = z*z;
+	r = S3+z*S4;
+	s = z*x;
+	return (x + s*(S1+z*S2)) + s*w*r;
 }