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, 15 insertions, 11 deletions

diff --git a/lib/msun/ld128/s_exp2l.c b/lib/msun/ld128/s_exp2l.c
index 28a6935..a94b892 100644
--- a/lib/msun/ld128/s_exp2l.c
+++ b/lib/msun/ld128/s_exp2l.c
@@ -356,8 +356,8 @@ static const float eps[TBLSIZE] = {
 long double
 exp2l(long double x)
 {
-	union IEEEl2bits u;
-	long double r, t, z;
+	union IEEEl2bits u, v;
+	long double r, t, twopk, twopkp10000, z;
 	uint32_t hx, ix, i0;
 	int k;
 
@@ -403,6 +403,15 @@ exp2l(long double x)
 	i0 = i0 & (TBLSIZE - 1);
 	u.e -= redux;
 	z = x - u.e;
+	v.xbits.manh = 0;
+	v.xbits.manl = 0;
+	if (k >= LDBL_MIN_EXP) {
+		v.xbits.expsign = LDBL_MAX_EXP - 1 + k;
+		twopk = v.e;
+	} else {
+		v.xbits.expsign = LDBL_MAX_EXP - 1 + k + 10000;
+		twopkp10000 = v.e;
+	}
 
 	/* Compute r = exp2(y) = exp2t[i0] * p(z - eps[i]). */
 	t = tbl[i0];		/* exp2t[i0] */
@@ -412,15 +421,10 @@ exp2l(long double x)
 
 	/* Scale by 2**k. */
 	if(k >= LDBL_MIN_EXP) {
-		if (k != 0) {
-			u.e = r;
-			u.xbits.expsign += k;
-			r = u.e;
-		}
-		return (r);
+		if (k == LDBL_MAX_EXP)
+			return (r * 2.0 * 0x1p16383L);
+		return (r * twopk);
 	} else {
-		u.e = r;
-		u.xbits.expsign += k + 10000;
-		return (u.e * twom10000);
+		return (r * twopkp10000 * twom10000);
 	}
 }