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, 7 insertions, 3 deletions

diff --git a/src/math/tanhf.c b/src/math/tanhf.c
index 8099ec30..10636fbd 100644
--- a/src/math/tanhf.c
+++ b/src/math/tanhf.c
@@ -17,7 +17,7 @@ float tanhf(float x)
 		/* |x| > log(3)/2 ~= 0.5493 or nan */
 		if (w > 0x41200000) {
 			/* |x| > 10 */
-			t = 1 + 0/(x + 0x1p-120f);
+			t = 1 + 0/x;
 		} else {
 			t = expm1f(2*x);
 			t = 1 - 2/(t+2);
@@ -26,10 +26,14 @@ float tanhf(float x)
 		/* |x| > log(5/3)/2 ~= 0.2554 */
 		t = expm1f(2*x);
 		t = t/(t+2);
-	} else {
-		/* |x| is small */
+	} else if (w >= 0x00800000) {
+		/* |x| >= 0x1p-126 */
 		t = expm1f(-2*x);
 		t = -t/(t+2);
+	} else {
+		/* |x| is subnormal */
+		FORCE_EVAL(x*x);
+		t = x;
 	}
 	return sign ? -t : t;
 }