Half-Precision Floating Point

On ARM and AArch64 targets, GCC supports half-precision (16-bit) floating point via the __fp16 type defined in the ARM C Language Extensions. On ARM systems, you must enable this type explicitly with the -mfp16-format command-line option in order to use it. On x86 targets with SSE2 enabled, GCC supports half-precision (16-bit) floating point via the _Float16 type. For C++, x86 provides a builtin type named _Float16 which contains same data format as C.

ARM targets support two incompatible representations for half-precision floating-point values. You must choose one of the representations and use it consistently in your program.

Specifying -mfp16-format=ieee selects the IEEE 754-2008 format. This format can represent normalized values in the range of 2^{-14} to 65504. There are 11 bits of significand precision, approximately 3 decimal digits.

Specifying -mfp16-format=alternative selects the ARM alternative format. This representation is similar to the IEEE format, but does not support infinities or NaNs. Instead, the range of exponents is extended, so that this format can represent normalized values in the range of 2^{-14} to 131008.

The GCC port for AArch64 only supports the IEEE 754-2008 format, and does not require use of the -mfp16-format command-line option.

The __fp16 type may only be used as an argument to intrinsics defined in <arm_fp16.h>, or as a storage format. For purposes of arithmetic and other operations, __fp16 values in C or C++ expressions are automatically promoted to float.

The ARM target provides hardware support for conversions between __fp16 and float values as an extension to VFP and NEON (Advanced SIMD), and from ARMv8-A provides hardware support for conversions between __fp16 and double values. GCC generates code using these hardware instructions if you compile with options to select an FPU that provides them; for example, -mfpu=neon-fp16 -mfloat-abi=softfp, in addition to the -mfp16-format option to select a half-precision format.

Language-level support for the __fp16 data type is independent of whether GCC generates code using hardware floating-point instructions. In cases where hardware support is not specified, GCC implements conversions between __fp16 and other types as library calls.

It is recommended that portable code use the _Float16 type defined by ISO/IEC TS 18661-3:2015. See Additional Floating Types.

On x86 targets with SSE2 enabled, without -mavx512fp16, all operations will be emulated by software emulation and the float instructions. The default behavior for FLT_EVAL_METHOD is to keep the intermediate result of the operation as 32-bit precision. This may lead to inconsistent behavior between software emulation and AVX512-FP16 instructions. Using -fexcess-precision=16 will force round back after each operation.

Using -mavx512fp16 will generate AVX512-FP16 instructions instead of software emulation. The default behavior of FLT_EVAL_METHOD is to round after each operation. The same is true with -fexcess-precision=standard and -mfpmath=sse. If there is no -mfpmath=sse, -fexcess-precision=standard alone does the same thing as before, It is useful for code that does not have _Float16 and runs on the x87 FPU.