sycl::half arithmetic operator promotes results to float

[TApplencourt]

Describe the bug

sycl::half arithmetic operator promotes results to float

To Reproduce

$cat test.cpp
#include <type_traits>
#include <sycl/sycl.hpp>
int main() {
   sycl::queue myQueue;
   myQueue.submit([&](sycl::handler& cgh) {
    sycl::device dev = myQueue.get_device();
    if (dev.has(sycl::aspect::fp16)) {
       cgh.single_task([=]{
            static_assert(std::is_same_v<decltype(sycl::half(1)), sycl::half>,"Not a sycl::half");
            static_assert(std::is_same_v<decltype(sycl::half(1) *  sycl::half(1) ), sycl::half>,"Not a sycl::half");
     });
    };
   });
   return 0;
}
$dpcpp test.cpp
test.cpp:11:13: error: static_assert failed due to requirement 'std::is_same_v<float, sycl::detail::half_impl::half>' "Not a sycl::half"
            static_assert(std::is_same_v<decltype(sycl::half(1) *  sycl::half(1) ), sycl::half>,"Not a sycl::half");
            ^             ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1 error generated.

Environment (please complete the following information):

• OS: Linux
• Target device and vendor: Intel GPU
• DPC++ version: Intel(R) oneAPI DPC++/C++ Compiler 2022.1.0 (2022.1.0.20220224)

[TApplencourt]

( @AerialMantis The "bug" --maybe it's not one, I didn't find anything in the spec, or in the OpenCL one, regarding half operation-- was found when porting sycl::complex to half-precision)

[zjin-lcf]

the cuda programming guide shows the fp16 operations.

__device__​ __half __hmul ( const __half a, const __half b )
Performs half multiplication in round-to-nearest-even mode.
Description
Performs half multiplication of inputs a and b, in round-to-nearest mode.

__device__​ __half __hmul_rn ( const __half a, const __half b )
Performs half multiplication in round-to-nearest-even mode.
Description
Performs half multiplication of inputs a and b, in round-to-nearest mode. Prevents floating-point contractions of mul+add or sub into fma.

__device__​ __half __hmul_sat ( const __half a, const __half b )
Performs half multiplication in round-to-nearest-even mode, with saturation to [0.0, 1.0].
Description
Performs half multiplication of inputs a and b, in round-to-nearest mode, and clamps the result to range [0.0, 1.0]. NaN results are flushed to +0.0.

[AidanBeltonS]

I have looked into this issue and can reproduce the error.
The problem is that there are some missing operators.
So the operators +-*/ were functioning via the implicit conversion to floating point type.

I have proposed a solution in #6061

[TApplencourt]

Thanks a lot!