Use a better method of scaling by 2**k. Instead of adding to the

exponent bits of the reduced result, construct 2**k (hopefully in
parallel with the construction of the reduced result) and multiply by
it.  This tends to be much faster if the construction of 2**k is
actually in parallel, and might be faster even with no parallelism
since adjustment of the exponent requires a read-modify-wrtite at an
unfortunate time for pipelines.

In some cases involving exp2* on amd64 (A64), this change saves about
40 cycles or 30%.  I think it is inherently only about 12 cycles faster
in these cases and the rest of the speedup is from partly-accidentally
avoiding compiler pessimizations (the construction of 2**k is now
manually scheduled for good results, and -O2 doesn't always mess this
up).  In most cases on amd64 (A64) and i386 (A64) the speedup is about
20 cycles.  The worst case that I found is expf on ia64 where this
change is a pessimization of about 10 cycles or 5%.  The manual
scheduling for plain exp[f] is harder and not as tuned.

This change ld128/s_exp2l.c has not been tested.

1 files changed, 3 insertions, 6 deletions

diff --git a/lib/msun/src/s_exp2f.c b/lib/msun/src/s_exp2f.c
index ffe58a2..d0f6b2f 100644
--- a/lib/msun/src/s_exp2f.c
+++ b/lib/msun/src/s_exp2f.c
@@ -92,7 +92,7 @@ static const double exp2ft[TBLSIZE] = {
 float
 exp2f(float x)
 {
-	double tv;
+	double tv, twopk;
 	float t, z;
 	uint32_t hx, htv, ix, i0;
 	int32_t k;
@@ -129,9 +129,6 @@ exp2f(float x)
 	tv = tv + tv * (z * (P1 + z * (P2 + z * (P3 + z * P4))));
 
 	/* Scale by 2**(k>>20). */
-	if (k != 0) {
-		GET_HIGH_WORD(htv, tv);
-		SET_HIGH_WORD(tv, htv + k);
-	}
-	return (tv);
+	INSERT_WORDS(twopk, 0x3ff00000 + k, 0);
+	return (tv * twopk);
 }