intermediate denormal numbers?

[kkimdev]

I guess denormals can appear in intermediate variables. But not all architectures support denormal, or denormal can be disabled by user with FTZ flag. Have we reviewed precision for such cases?

[shibatch]

Denormals should be treated correctly. Please check the source code for tester2*.c. A few functions cannot handle denormals very well. For those functions, the error range is specified as max(DBL_MIN, xxULPs).

[kkimdev]

Just to clarify: even if input x is not a denormal number, for example, I guess the following two functions can result different outputs, because denormal numbers can appear during computation.

_MM_SET_DENORMALS_ZERO_MODE(_MM_DENORMALS_ZERO_ON);
_MM_SET_FLUSH_ZERO_MODE(_MM_FLUSH_ZERO_ON);
// x is not necessarily denormal
xsinf(x);

_MM_SET_DENORMALS_ZERO_MODE(_MM_DENORMALS_ZERO_OFF);
_MM_SET_FLUSH_ZERO_MODE(_MM_FLUSH_ZERO_OFF);
// x is not necessarily denormal
xsinf(x);

Perhaps supporting FTZ/DAZ flags == ON is out of the scope, but to my understanding some architectures don't support denormals at all (ARM Neon?). Likely it's not a big issue but I think it's good to review that if there is some difference between FTZ/DAZ on & off.

[shibatch]

Although it is not mentioned, SLEEF implicitly assumes IEEE 754 compliance. For AARCH32, flush to zero mode is supported in an ad-hoc way.