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.)

3 files changed, 46 insertions, 7 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
diff --git a/src/math/i386/scalbnf.s b/src/math/i386/scalbnf.s
index 40232b6a..9cb9ef5f 100644
--- a/src/math/i386/scalbnf.s
+++ b/src/math/i386/scalbnf.s
@@ -11,10 +11,22 @@ scalblnf:
 .global scalbnf
 .type scalbnf,@function
 scalbnf:
-	fildl 8(%esp)
+	mov 8(%esp),%eax
+	add $0x3fe,%eax
+	cmp $0x7fd,%eax
+	jb 1f
+	sub $0x3fe,%eax
+	sar $31,%eax
+	xor $0x1ff,%eax
+	add $0x3fe,%eax
+1:	inc %eax
+	shl $20,%eax
 	flds 4(%esp)
-	fscale
-	fstp %st(1)
+	mov %eax,8(%esp)
+	xor %eax,%eax
+	mov %eax,4(%esp)
+	fldl 4(%esp)
+	fmulp
 	fstps 4(%esp)
 	flds 4(%esp)
 	ret
diff --git a/src/math/i386/scalbnl.s b/src/math/i386/scalbnl.s
index 224b1bef..54414c2e 100644
--- a/src/math/i386/scalbnl.s
+++ b/src/math/i386/scalbnl.s
@@ -11,7 +11,21 @@ scalblnl:
 .global scalbnl
 .type scalbnl,@function
 scalbnl:
-	fildl 16(%esp)
+	mov 16(%esp),%eax
+	add $0x3ffe,%eax
+	cmp $0x7ffd,%eax
+	jae 1f
+	inc %eax
+	fldt 4(%esp)
+	mov %eax,12(%esp)
+	mov $0x80000000,%eax
+	mov %eax,8(%esp)
+	xor %eax,%eax
+	mov %eax,4(%esp)
+	fldt 4(%esp)
+	fmulp
+	ret
+1:	fildl 16(%esp)
 	fldt 4(%esp)
 	fscale
 	fstp %st(1)