Bfloat16 floating-point format

The bfloat16 (brain floating point) floating-point format is a computer number format occupying 16 bits in computer memory; it represents a wide dynamic range of numeric values by using a floating radix point. This format is a shortened (16-bit) version of the 32-bit IEEE 754 single-precision floating-point format (binary32) with the intent of accelerating machine learning and near-sensor computing. It preserves the approximate dynamic range of 32-bit floating-point numbers by retaining 8 exponent bits, but supports only an 8-bit precision rather than the 24-bit significand of the binary32 format. More so than single-precision 32-bit floating-point numbers, bfloat16 numbers are unsuitable for integer calculations, but this is not their intended use. Bfloat16 is used to reduce the storage requirements and increase the calculation speed of machine learning algorithms.

The bfloat16 format was developed by Google Brain, an artificial intelligence research group at Google. It is utilized in many CPUs, GPUs, and AI processors, such as Intel Xeon processors (AVX-512 BF16 extensions), Intel Data Center GPU, Intel Nervana NNP-L1000, Intel FPGAs, AMD Zen, AMD Instinct, NVIDIA GPUs, Google Cloud TPUs, AWS Inferentia, AWS Trainium, ARMv8.6-A, and Apple's M2 and therefore A15 chips and later. Many libraries support bfloat16, such as CUDA, Intel oneAPI Math Kernel Library, AMD ROCm, AMD Optimizing CPU Libraries, PyTorch, and TensorFlow. On these platforms, bfloat16 may also be used in mixed-precision arithmetic, where bfloat16 numbers may be operated on and expanded to wider data types.

bfloat16 has the following format:

The bfloat16 format, being a shortened IEEE 754 single-precision 32-bit float, allows for fast conversion to and from an IEEE 754 single-precision 32-bit float; in conversion to the bfloat16 format, the exponent bits are preserved while the significand field can be reduced by truncation (thus corresponding to round toward 0) or other rounding mechanisms, ignoring the NaN special case. Preserving the exponent bits maintains the 32-bit float's range of ≈ 10⁻³⁸ to ≈ 3 × 10³⁸.

The bits are laid out as follows:

The bfloat16 binary floating-point exponent is encoded using an offset-binary representation, with the zero offset being 127; also known as exponent bias in the IEEE 754 standard.

Thus, in order to get the true exponent as defined by the offset-binary representation, the offset of 127 has to be subtracted from the value of the exponent field.

The minimum and maximum values of the exponent field (00_H and FF_H) are interpreted specially, like in the IEEE 754 standard formats.