math: fix asin, atan, log1p, tanh to raise underflow on subnormal

for these functions f(x)=x for small inputs, because f(0)=0 and
f'(0)=1, but for subnormal values they should raise the underflow
flag (required by annex F), if they are approximated by a polynomial
around 0 then spurious underflow should be avoided (not required by
annex F)

all these functions should raise inexact flag for small x if x!=0,
but it's not required by the standard and it does not seem a worthy
goal, so support for it is removed in some cases.

raising underflow:
- x*x may not raise underflow for subnormal x if FLT_EVAL_METHOD!=0
- x*x may raise spurious underflow for normal x if FLT_EVAL_METHOD==0
- in case of double subnormal x, store x as float
- in case of float subnormal x, store x*x as float

1 files changed, 3 insertions, 4 deletions

diff --git a/src/math/asinf.c b/src/math/asinf.c
index 51fe6c61..bcd304a3 100644
--- a/src/math/asinf.c
+++ b/src/math/asinf.c
@@ -46,10 +46,9 @@ float asinf(float x)
 		return 0/(x-x);  /* asin(|x|>1) is NaN */
 	}
 	if (ix < 0x3f000000) {  /* |x| < 0.5 */
-		if (ix < 0x39800000) {  /* |x| < 2**-12 */
-			FORCE_EVAL(x + 0x1p120f);
-			return x; /* return x with inexact if x!=0 */
-		}
+		/* if 0x1p-126 <= |x| < 0x1p-12, avoid raising underflow */
+		if (ix < 0x39800000 && ix >= 0x00800000)
+			return x;
 		return x + x*R(x*x);
 	}
 	/* 1 > |x| >= 0.5 */