math: change the formula used for acos.s

old: 2*atan2(sqrt(1-x),sqrt(1+x))
new: atan2(fabs(sqrt((1-x)*(1+x))),x)
improvements:
* all edge cases are fixed (sign of zero in downward rounding)
* a bit faster (here a single call is about 131ns vs 162ns)
* a bit more precise (at most 1ulp error on 1M uniform random
samples in [0,1), the old formula gave some 2ulp errors as well)

src/math/i386/acos.s

@@ -1,3 +1,5 @@
+# use acos(x) = atan2(fabs(sqrt((1-x)*(1+x))), x)
+
 .global acosf
 .type acosf,@function
 acosf:
@@ -14,17 +16,13 @@ acosl:
 .type acos,@function
 acos:
 	fldl 4(%esp)
-1:	fld1
-	fld %st(1)
+1:	fld %st(0)
 	fld1
-	fsubp
-	fsqrt
-	fxch %st(2)
-	faddp
+	fsub %st(0),%st(1)
+	fadd %st(2)
+	fmulp
 	fsqrt
+	fabs         # fix sign of zero (matters in downward rounding mode)
+	fxch %st(1)
 	fpatan
-	fld1
-	fld1
-	faddp
-	fmulp
 	ret

src/math/x86_64/acosl.s

@@ -1,18 +1,16 @@
+# see ../i386/acos.s
+
 .global acosl
 .type acosl,@function
 acosl:
 	fldt 8(%rsp)
+1:	fld %st(0)
 	fld1
-	fld %st(1)
-	fld1
-	fsubp
-	fsqrt
-	fxch %st(2)
-	faddp
+	fsub %st(0),%st(1)
+	fadd %st(2)
+	fmulp
 	fsqrt
+	fabs
+	fxch %st(1)
 	fpatan
-	fld1
-	fld1
-	faddp
-	fmulp
 	ret