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, 9 insertions, 5 deletions

diff --git a/src/math/tanh.c b/src/math/tanh.c
index 0e766c5c..20d6dbcf 100644
--- a/src/math/tanh.c
+++ b/src/math/tanh.c
@@ -9,7 +9,7 @@ double tanh(double x)
 	union {double f; uint64_t i;} u = {.f = x};
 	uint32_t w;
 	int sign;
-	double t;
+	double_t t;
 
 	/* x = |x| */
 	sign = u.i >> 63;
@@ -22,8 +22,7 @@ double tanh(double x)
 		if (w > 0x40340000) {
 			/* |x| > 20 or nan */
 			/* note: this branch avoids raising overflow */
-			/* raise inexact if x!=+-inf and handle nan */
-			t = 1 + 0/(x + 0x1p-120f);
+			t = 1 - 0/x;
 		} else {
 			t = expm1(2*x);
 			t = 1 - 2/(t+2);
@@ -32,10 +31,15 @@ double tanh(double x)
 		/* |x| > log(5/3)/2 ~= 0.2554 */
 		t = expm1(2*x);
 		t = t/(t+2);
-	} else {
-		/* |x| is small, up to 2ulp error in [0.1,0.2554] */
+	} else if (w >= 0x00100000) {
+		/* |x| >= 0x1p-1022, up to 2ulp error in [0.1,0.2554] */
 		t = expm1(-2*x);
 		t = -t/(t+2);
+	} else {
+		/* |x| is subnormal */
+		/* note: the branch above would not raise underflow in [0x1p-1023,0x1p-1022) */
+		FORCE_EVAL((float)x);
+		t = x;
 	}
 	return sign ? -t : t;
 }