optimize scalbn family

the fscale instruction is slow everywhere, probably because it
involves a costly and unnecessary integer truncation operation that
ends up being a no-op in common usages. instead, construct a floating
point scale value with integer arithmetic and simply multiply by it,
when possible.

for float and double, this is always possible by going to the
next-larger type. we use some cheap but effective saturating
arithmetic tricks to make sure even very large-magnitude exponents
fit. for long double, if the scaling exponent is too large to fit in
the exponent of a long double value, we simply fallback to the
expensive fscale method.

on atom cpu, these changes speed up scalbn by over 30%. (min rdtsc
timing dropped from 110 cycles to 70 cycles.)

1 files changed, 16 insertions, 3 deletions

diff --git a/src/math/i386/scalbn.s b/src/math/i386/scalbn.s
index e275d14f..8bf302f2 100644
--- a/src/math/i386/scalbn.s
+++ b/src/math/i386/scalbn.s
@@ -11,10 +11,23 @@ scalbln:
 .global scalbn
 .type scalbn,@function
 scalbn:
-	fildl 12(%esp)
+	mov 12(%esp),%eax
+	add $0x3ffe,%eax
+	cmp $0x7ffd,%eax
+	jb 1f
+	sub $0x3ffe,%eax
+	sar $31,%eax
+	xor $0xfff,%eax
+	add $0x3ffe,%eax
+1:	inc %eax
 	fldl 4(%esp)
-	fscale
-	fstp %st(1)
+	mov %eax,12(%esp)
+	mov $0x80000000,%eax
+	mov %eax,8(%esp)
+	xor %eax,%eax
+	mov %eax,4(%esp)
+	fldt 4(%esp)
+	fmulp
 	fstpl 4(%esp)
 	fldl 4(%esp)
 	ret