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
This commit is contained in:
Szabolcs Nagy
2013-08-15 10:14:46 +00:00
parent cd18dc8525
commit c599f4f4d7
9 changed files with 39 additions and 26 deletions

View File

@ -23,8 +23,8 @@ double sinh(double x)
t = expm1(absx);
if (w < 0x3ff00000) {
if (w < 0x3ff00000 - (26<<20))
/* note: inexact is raised by expm1 */
/* note: this branch avoids underflow */
/* note: inexact and underflow are raised by expm1 */
/* note: this branch avoids spurious underflow */
return x;
return h*(2*t - t*t/(t+1));
}