Replace usage of `std::numeric_limits<...>::min/max_exponent` in
codebase where possible. Also replaced some other `numeric_limits`
usages in affected tests with the `NumTraits` equivalent.
The previous MR !443 failed for c++03 due to lack of `constexpr`.
Because of this, we need to keep around the `std::numeric_limits`
version in enum expressions until the switch to c++11.
Fixes#2148
Replace usage of `std::numeric_limits<...>::min/max_exponent` in
codebase. Also replaced some other `numeric_limits` usages in
affected tests with the `NumTraits` equivalent.
Fixes#2148
Since `numeric_limits<half>::max_exponent` is a static inline constant,
it cannot be directly passed by reference. This triggers a linker error
in recent versions of `g++-powerpc64le`.
Changing `half` to take inputs by value fixes this. Wrapping
`max_exponent` with `int(...)` to make an addressable integer also fixes this
and may help with other custom `Scalar` types down-the-road.
Also eliminated some compile warnings for powerpc.
The new `generic_pow` implementation was failing for half/bfloat16 since
their construction from int/float is not `constexpr`. Modified
in `GenericPacketMathFunctions` to remove `constexpr`.
While adding tests for half/bfloat16, found other issues related to
implicit conversions.
Also needed to implement `numext::arg` for non-integer, non-complex,
non-float/double/long double types. These seem to be implicitly
converted to `std::complex<T>`, which then fails for half/bfloat16.
I ran some testing (comparing to `std::pow(double(x), double(y)))` for `x` in the set of all (positive) floats in the interval `[std::sqrt(std::numeric_limits<float>::min()), std::sqrt(std::numeric_limits<float>::max())]`, and `y` in `{2, sqrt(2), -sqrt(2)}` I get the following error statistics:
```
max_rel_error = 8.34405e-07
rms_rel_error = 2.76654e-07
```
If I widen the range to all normal float I see lower accuracy for arguments where the result is subnormal, e.g. for `y = sqrt(2)`:
```
max_rel_error = 0.666667
rms = 6.8727e-05
count = 1335165689
argmax = 2.56049e-32, 2.10195e-45 != 1.4013e-45
```
which seems reasonable, since these results are subnormals with only couple of significant bits left.
This provides a new op that matches std::rint and previous behavior of
pround. Also adds corresponding unsupported/../Tensor op.
Performance is the same as e. g. floor (tested SSE/AVX).
