math: fix x86 asin accuracy

use (1-x)*(1+x) instead of (1-x*x) in asin.s
the later can be inaccurate with upward rounding when x is close to 1

diff --git a/src/math/i386/asin.s b/src/math/i386/asin.s
index cab7bfc84466cf63d220bc6824c380577addd413..932c7542442787f30361489b3f4e9d57fed7ffec 100644 (file)
--- a/src/math/i386/asin.s
+++ b/src/math/i386/asin.s
@@ -15,9 +15,10 @@ asinl:
 asin:
        fldl 4(%esp)
 1:     fld %st(0)
-       fmul %st(0)
        fld1
-       fsubp %st(1)
+       fsub %st(0),%st(1)
+       fadd %st(2)
+       fmulp
        fsqrt
        fpatan
        ret

diff --git a/src/math/x86_64/asinl.s b/src/math/x86_64/asinl.s
index 83c392f761986d1c76859e34e38e5efb7922b6fd..ed212d9a6c173855c26d8d9428ff8a38cb5d5819 100644 (file)
--- a/src/math/x86_64/asinl.s
+++ b/src/math/x86_64/asinl.s
@@ -3,10 +3,10 @@
 asinl:
        fldt 8(%rsp)
 1:     fld %st(0)
-       fmul %st(0)
        fld1
-       fsubp %st(1)
+       fsub %st(0),%st(1)
+       fadd %st(2)
+       fmulp
        fsqrt
        fpatan
        ret
-