In libm, sin(qNaN) doesn't expect FE_INVALID ?

[Joseph Myers]

On Tue, 8 Sep 2020, Ruinland ChuanTzu Tsai wrote:

> If I may, I have another question upon sin,atan(±0x4p-1076), the test-
> suite expects FE_UNDERFLOW being raised.
> 
> In `math/libm-test-{sin,atan}.inc` , I cannot see the corresponding
> expectation being set.  

That's because tests with finite inputs and finite mathematical results 
(possibly overflowing the floating-point type) generally go in 
auto-libm-test-in to have the expected results generated automatically by 
gen-auto-libm-tests; libm-test-*.inc are mainly for cases where the inputs 
or results involve exact infinities or NaNs.

> if (k < 0x3e500000)       /* if x->0 =>sin(x)=x */
>   {
>     math_check_force_underflow (x);
>     retval = x;
>   }
> ```
> 
> I've read IEEE Standard Section 7.5 which regulates that if a tiny non-
> zero number is detected, an exception shall be raised. However I'm not
> so sure about the reason why the magic number is set to `0x3e500000`.

That is a check for whether the argument is small enough that the argument 
itself is an accurate return value (then math_check_force_underflow does 
the separate check for whether it's small enough that the underflow 
exception must be raised).  As sin(x) = x - x^3/6 + ..., if x^2/6 is 
around 2^-54 or smaller, the error from returning x as the result is 
small.  That reasoning leads to the comparison of the leading bits of the 
representation against 0x3e500000 (i.e. comparing |x| against 0x1p-26).

-- 
Joseph S. Myers
joseph@codesourcery.com