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IEEE float16 related functions

NSIMD natively supports IEEE float16's. This means that NSIMD provides types and functions to deal with them. When the targeted architecture supports them then NSIMD will use approriate intrinsics otherwise emulation with float32's will be used.

• When emulating, as float16's are not natively supported by neither C or C++ emulation is done with float32's.

• Intel architectures do not support IEEE float16 arithmetic, they only provide, as an extension, supports for convertion to/from float32. When compiling NSIMD for Intel architectures use -DFP16 to activate the conversion intrinsics if available on your machine. Note that AVX-512 has thoses natively.

• Arm architectures can provide native float16 arithmetic. For 32-bits and 64-bits chips (ARMv7 and Aarch64) chips float16 support is optional. When compiling with -DFP16, NSIMD will use float16-related intrinsics. Note that for SVE chips float16's are mandatory hence NSIMD will use appropriate intrinsics with or without -DFP16.

• CUDA provides supports for converting float16's to/from float32's. These are always used by NSIMD. But it is only since devices of compute capabilities 5.3 and above that float16's arithmetic is provided. NSIMD will always use CUDA float16's functions so there is no need to compile with -DFP16.

• ROCm HIP supports float16's except for the first versions. For now NSIMD assumes that it is always the case and use HIP float16 API. There is no need for -DFP16.

Float16's related functions and types

NSIMD provide the f16 type which represents a IEEE float16. Note that depending on the targeted architecture and the presence of -DFP16 the float16 type can typedefs many different types. Therefore the two following functions are provided and can be used to convert a float16 from/to a float32. These functions preserve NaN's and infinities. When converting from a float32 to a float16 saturation to infinities is performed when the float32 cannot be represented as a float16.

For loading/storing float16's NSIMD provides other conversion function to/from 16-bits unsigned integers. The integers will hold the IEEE binary representation of the float16's.

The nsimd_* functions listed above do not use the same linkage type depending on the targeted architecture. When compiling for GPUs the corresponding symbols names are mangled. They use C++ ABI because the float16 type is defined as a C++ class and not as a C struct. We therefore inherit from the implementation of CUDA and HIP/ROCm. Linkage types are listed below.

It is possible to know at compile time in which situation we are. The NSIMD_C_LINKAGE_FOR_F16 macro if defined means that C linkage is used for nsimd_* functions.