Support for bfloat16

[tisnik]

Thank you for making this very useful and well-tested library! Are you planning to add support for bfloat16 format, which is used in ML field? It has different bit widths for mantissa and exponent, but other rules are the same as in IEEE 754 formats.

[x448]

Hi Pavel, I took a quick glance at bfloat16. If I implement it, I think it would be in a separate project.

There would have to be a convenient way for me to compare results with a hardware implementation. I'd like to be able to confirm 100% of float32<-->bfloat16 conversions.

float16 was very convenient because the vm I use for coding had hardware instructions (F16C aka FP16C).

[tisnik]

Thank you for a quick response. Yes, it totally make sense to create bfloat16 as separate project (thought IMHO most of the code will be very similar). As far as I know, bfloat16 is supported in AVX-512 - VCVTNE2PS2BF16, VCVTNEPS2BF16 and
VDPBF16PS instructions, but I have not tried them (and very probably it won't be possible to use Go assembler with those pretty new instructions). I planned to create some conversion library myself, but I'm not sure how to handle special cases like denormalized values, sNaNs, qNaNs etc. as some bfloat16 implementations don't follow all IEEE 754 rules.

[agj32mrgibbits]

Looks to me like bfloat16 conversion between float32 is a simple and fast shift:

type BFloat16 uint16

func ToFloat32(x BFloat16) float32 {
	return math.Float32frombits(uint32(x) << 16)
}

func FromFloat32(x float32) BFloat16 {
	return BFloat16(math.Float32bits(x) >> 16)
}

func FromBits(u16 uint16) BFloat16 {
	return BFloat16(u16)
}

func Bits(f BFloat16) uint16 {
	return uint16(f)
}

func (f BFloat16) String() string {
	return strconv.FormatFloat(float64(ToFloat32(f)), 'f', -1, 32)
}

https://go.dev/play/p/jhXQvuI9Pxz

[fxamacker]

Support for bfloat16 is also requested in comments at #46

[x448]

bfloat16 and patents:

• https://en.wikipedia.org/wiki/Tensor_Processing_Unit#Lawsuit
• https://www.reddit.com/r/MachineLearning/comments/193zpyi/d_does_patent_lawsuit_against_googles_tpu_imperil/