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, 2 insertions, 4 deletions

diff --git a/src/math/asin.c b/src/math/asin.c
index 3e8f99ed..c926b188 100644
--- a/src/math/asin.c
+++ b/src/math/asin.c
@@ -82,11 +82,9 @@ double asin(double x)
 	}
 	/* |x| < 0.5 */
 	if (ix < 0x3fe00000) {
-		if (ix < 0x3e500000) {
-			/* |x|<0x1p-26, return x with inexact if x!=0*/
-			FORCE_EVAL(x + 0x1p120f);
+		/* if 0x1p-1022 <= |x| < 0x1p-26, avoid raising underflow */
+		if (ix < 0x3e500000 && ix >= 0x00100000)
 			return x;
-		}
 		return x + x*R(x*x);
 	}
 	/* 1 > |x| >= 0.5 */