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fixes #79
Question remains @oscardssmith: Why write (1)
and not just (2)
?
From a precision perspective they are the same (no rounding errors in
BFloat16
arithmetic because you exactly hit eps/2, eps, 3eps/2, n*eps/2 which are all perfectly representable) but in (1) the actual multiplication is hardcoded inFloat32
which avoids the conversion from
BFloat16(0x1.0p-8)
toFloat32
ifBFloat16
is not natively supported, I believe? Meaning it's probably faster ifbfloat16
is not natively supported. Whereas with (2) we would have the advantage that LLVM'sbfloat
type would decide what to do depending on the hardware meaning it would be faster on devices withbfloat16
support (as multiplication is then not done withFloat32
?)