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, 8 insertions, 9 deletions

diff --git a/lib/msun/src/e_exp.c b/lib/msun/src/e_exp.c
index 60b8b2a..0809c66 100644
--- a/lib/msun/src/e_exp.c
+++ b/lib/msun/src/e_exp.c
@@ -102,7 +102,7 @@ P5   =  4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */
 double
 __ieee754_exp(double x)	/* default IEEE double exp */
 {
-	double y,hi=0.0,lo=0.0,c,t;
+	double y,hi=0.0,lo=0.0,c,t,twopk;
 	int32_t k=0,xsb;
 	u_int32_t hx;
 
@@ -142,18 +142,17 @@ __ieee754_exp(double x)	/* default IEEE double exp */
 
     /* x is now in primary range */
 	t  = x*x;
+	if(k >= -1021)
+	    INSERT_WORDS(twopk,0x3ff00000+(k<<20), 0);
+	else
+	    INSERT_WORDS(twopk,0x3ff00000+((k+1000)<<20), 0);
 	c  = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
 	if(k==0) 	return one-((x*c)/(c-2.0)-x); 
 	else 		y = one-((lo-(x*c)/(2.0-c))-hi);
 	if(k >= -1021) {
-	    u_int32_t hy;
-	    GET_HIGH_WORD(hy,y);
-	    SET_HIGH_WORD(y,hy+(k<<20));	/* add k to y's exponent */
-	    return y;
+	    if (k==1024) return y*2.0*0x1p1023;
+	    return y*twopk;
 	} else {
-	    u_int32_t hy;
-	    GET_HIGH_WORD(hy,y);
-	    SET_HIGH_WORD(y,hy+((k+1000)<<20));	/* add k to y's exponent */
-	    return y*twom1000;
+	    return y*twopk*twom1000;
 	}
 }