`Base.issubnormal(::BFloat16)` is missing

[dzhang314]

The floating-point introspection function issubnormal(x) is not implemented for x::BFloat16. Since BFloat16 has the same exponent range as Float32, I suggest the following implementation:

@inline Base.issubnormal(x::BFloat16) = issubnormal(Float32(x))

This compiles to nice, clean assembly, at least on arm:

	.build_version macos, 15, 0
	.globl	_julia_issubnormal_42           ; -- Begin function julia_issubnormal_42
	.p2align	2
_julia_issubnormal_42:                  ; @julia_issubnormal_42
; %bb.0:                                ; %top
	tst	w0, #0x7f80
	cset	w8, eq
	tst	w0, #0x7f
	cset	w9, ne
	and	w0, w8, w9
	ret
                                        ; -- End function
.subsections_via_symbols

[milankl]

Could we not just check that the exponent bits are all zero? i.e. Base.exponent_mask(BFloat16) & reinterpret(UInt16, x) == 0?

[dzhang314]

@milankl No; recall that zero has encoding 0x0000 or 0x8000 but is not considered subnormal. But I think you're right that iszero(Base.exponent_mask(BFloat16) & reinterpret(UInt16, x)) & ~iszero(x) is a correct implementation, and I think that is effectively what the generated assembly for issubnormal(Float32(x)) is doing.

[milankl]

Riiight my bad! But now I see what you mean by "clean", the conversion to Float32 (that I wanted to avoid) is indeed compiled away. Bit surprised to see that, but yes I would naively check for exponent = 0 and mantissa > 0. Not sure whether relying on the compiler translating to that is the best strategy though given we already know what we actually want to do in bitwise operations? Sure what you suggest is short but much less literal?

[milankl]

Actually you write ~iszero(x) but this line tst w0, #0x7f is Base.significand_mask(BFloat16) & ui no?

[dzhang314]

That's fair! I was also surprised to see the compiler could entirely reason away the conversion to Float32, and I also prefer not to rely too much on compiler optimization where it can be easily avoided. And you're right, exponent = 0 and mantissa != 0 is exactly what the generated assembly is checking for.

[dzhang314]

As another data point, this also generates good assembly on x86-64.

	.text
	.file	"issubnormal"
	.globl	julia_issubnormal_787           # -- Begin function julia_issubnormal_787
	.p2align	4, 0x90
	.type	julia_issubnormal_787,@function
julia_issubnormal_787:                  # @julia_issubnormal_787
# %bb.0:                                # %top
	push	rbp
	mov	rbp, rsp
	test	edi, 32640
	sete	cl
	test	dil, 127
	setne	al
	and	al, cl
	pop	rbp
	ret
.Lfunc_end0:
	.size	julia_issubnormal_787, .Lfunc_end0-julia_issubnormal_787
                                        # -- End function
	.section	".note.GNU-stack","",@progbits