Remove the "quick check no cancellation" optimization for

9pi/2 < |x| < 32pi/2 since it is only a small or negative optimation
and it gets in the way of further optimizations.  It did one more
branch to avoid some integer operations and to use a different
dependency on previous results.  The branches are fairly predictable
so they are usually not a problem, so whether this is a good
optimization depends mainly on the timing for the previous results,
which is very machine-dependent.  On amd64 (A64), this "optimization"
is a pessimization of about 1 cycle or 1%; on ia64, it is an
optimization of about 2 cycles or 1%; on i386 (A64), it is an
optimization of about 5 cycles or 4%; on i386 (Celeron P2) it is an
optimization of about 4 cycles or 3% for cos but a pessimization of
about 5 cycles for sin and 1 cycle for tan.  I think the new i386
(A64) slowness is due to an pipeline stall due to an avoidable
load-store mismatch (so the old timing was better), and the i386
(Celeron) variance is due to its branch predictor not being too good.

1 files changed, 1 insertions, 12 deletions

diff --git a/lib/msun/src/e_rem_pio2.c b/lib/msun/src/e_rem_pio2.c
index 0dc88f4..708b882 100644
--- a/lib/msun/src/e_rem_pio2.c
+++ b/lib/msun/src/e_rem_pio2.c
@@ -26,15 +26,6 @@ __FBSDID("$FreeBSD$");
 #include "math.h"
 #include "math_private.h"
 
-static const int32_t npio2_hw[] = {
-0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
-0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
-0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
-0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
-0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
-0x404858EB, 0x404921FB,
-};
-
 /*
  * invpio2:  53 bits of 2/pi
  * pio2_1:   first  33 bit of pi/2
@@ -148,9 +139,7 @@ medium:
 #endif
 	    r  = t-fn*pio2_1;
 	    w  = fn*pio2_1t;	/* 1st round good to 85 bit */
-	    if(n<32&&ix!=npio2_hw[n-1]) {	
-		y[0] = r-w;	/* quick check no cancellation */
-	    } else {
+	    {
 	        u_int32_t high;
 	        j  = ix>>20;
 	        y[0] = r-w;