[maleadt]

Before Julia 1.13 there is no LLVM bfloat arithmetic on Apple silicon, and BFloat16s converts from Float32 by rounding the bits as an integer: isnan(x) ? 0x7fc0 : (bits + bias) >> 16. Apple's back-end drops the shift of that select when its result is used as 32 bits. The IR and AIR Metal.jl emits are correct. Minimal case, without BFloat16 (macOS 27, M1):

k(out, a) = (i = thread_position_in_threadgroup().x; f = a[i] + a[i]; b = reinterpret(UInt32, f);
             out[i] = isnan(f) ? UInt32(0x7fc0) : b >> 16; return)
# returns 0x40000000 for a = ones(Float32, 32), instead of 0x00004000

Only an fcmp ord/uno condition combined with a logical shift right by 16 triggers it. Normally the result is truncated to i16 right away and nothing goes wrong, but anything that widens the bits gets them wrong:

• sum and prod of a BFloat16 array return NaN with GPUArrays main. Since Reduce with operators not known to commute in element order GPUArrays.jl#822 these reductions use AcceleratedKernels' ordered kernel, whose block scan shuffles the partial results. Metal has no shuffle for BFloat16, so KernelInterface's fallback shuffles the bits as a UInt32. This is the Metal 1.10 failure on GPUArrays main, Inline the range indexing kernel bodies and launch getindex linearly GPUArrays.jl#839 and Define neutral elements for the @fastmath reduction operators GPUArrays.jl#840.
• sum of a Complex{BFloat16} array is garbage already with the released GPUArrays (the shuffle fallback packs both fields into one word).
• map(x -> reinterpret(UInt16, x + x) % UInt32, a) returns the wrong bits.

On the emulated path, the device conversion now emits the fptrunc float to bfloat that the native path uses. Metal.jl requires macOS 15, so the conversion is available on every supported system. The conversion matched BFloat16s bit for bit on 2M inputs, including subnormals, infinities, signed zeros and rounding ties. The only difference is that NaN payloads are kept rather than normalized to 0x7fc0, as on the native path.

[github-actions]

Benchmark results

Compared with 0877ad5a3, the merge base.
The environment differs from the baseline's: GPUCompiler 2.18.0 → 2.19.0.

Times are the minimum time of every benchmark. A change is unusual when it exceeds both three times the benchmark's typical change between consecutive runs on the default branch and a minimum per category (performance 3%, latency 5%, applications 3%, other 3%). A benchmark that starts or stops allocating is listed however few the allocations. A single run can still be a fluke, so rerun before drawing conclusions.

	Geometric mean	Unusual: slower	Unusual: faster	Compared
Performance	−0.1%	1	1	74
Latency	−0.3%	0	0	4
Applications	+1.2%	1	0	5

Benchmark	Baseline	This PR	Change
Performance
array/random/randn!/Float32	357 µs	294 µs	−17.7%	🟢 faster
array/private/iteration/findfirst/bool	255 µs	283 µs	+11.2%	🔴 slower
Applications
metaldevrt	370 µs	393 µs	+6.1%	🔴 slower

All benchmarks

Benchmark	Baseline	This PR	Change
Performance
array/accumulate/Float32/1d	393 µs	392 µs	−0.3%
array/accumulate/Float32/dims=1	373 µs	364 µs	−2.5%
array/accumulate/Float32/dims=1L	8.87 ms	8.86 ms	−0.1%
array/accumulate/Float32/dims=2	436 µs	431 µs	−1.2%
array/accumulate/Float32/dims=2L	2.86 ms	2.69 ms	−6.0%
array/accumulate/Int64/1d	520 µs	526 µs	+1.1%
array/accumulate/Int64/dims=1	518 µs	521 µs	+0.5%
array/accumulate/Int64/dims=1L	1.64 ms	1.64 ms	+0.3%
array/accumulate/Int64/dims=2	540 µs	538 µs	−0.3%
array/accumulate/Int64/dims=2L	5.45 ms	5.43 ms	−0.3%
array/broadcast	238 µs	237 µs	−0.1%
array/construct	2.25 µs	2.21 µs	−1.9%
array/permutedims/2d	340 µs	338 µs	−0.6%
array/permutedims/3d	465 µs	461 µs	−0.8%
array/permutedims/4d	423 µs	420 µs	−0.6%
array/private/copy	226 µs	228 µs	+0.8%
array/private/copyto!/cpu_to_gpu	219 µs	224 µs	+2.3%
array/private/copyto!/gpu_to_cpu	224 µs	220 µs	−1.8%
array/private/copyto!/gpu_to_gpu	217 µs	219 µs	+0.6%
array/private/iteration/findall/bool	354 µs	356 µs	+0.4%
array/private/iteration/findall/int	428 µs	421 µs	−1.7%
array/private/iteration/findfirst/bool	255 µs	283 µs	+11.2%	🔴 slower
array/private/iteration/findfirst/int	283 µs	279 µs	−1.4%
array/private/iteration/findmin/1d	348 µs	347 µs	−0.2%
array/private/iteration/findmin/2d	389 µs	386 µs	−0.9%
array/private/iteration/logical	365 µs	364 µs	−0.2%
array/private/iteration/scalar	1.40 ms	1.34 ms	−3.9%
array/random/rand!/Float32	426 µs	427 µs	+0.2%
array/random/rand!/Int64	451 µs	447 µs	−1.1%
array/random/rand/Float32	444 µs	439 µs	−1.2%
array/random/rand/Int64	515 µs	514 µs	−0.2%
array/random/randn!/Float32	357 µs	294 µs	−17.7%	🟢 faster
array/random/randn/Float32	368 µs	364 µs	−0.9%
array/reductions/mapreduce/Float32/1d	214 µs	218 µs	+2.0%
array/reductions/mapreduce/Float32/dims=1	216 µs	213 µs	−1.0%
array/reductions/mapreduce/Float32/dims=1L	581 µs	579 µs	−0.5%
array/reductions/mapreduce/Float32/dims=2	256 µs	253 µs	−1.4%
array/reductions/mapreduce/Float32/dims=2L	423 µs	408 µs	−3.6%
array/reductions/mapreduce/Int64/1d	210 µs	230 µs	+9.3%
array/reductions/mapreduce/Int64/dims=1	218 µs	220 µs	+1.1%
array/reductions/mapreduce/Int64/dims=1L	998 µs	994 µs	−0.4%
array/reductions/mapreduce/Int64/dims=2	264 µs	259 µs	−2.0%
array/reductions/mapreduce/Int64/dims=2L	600 µs	599 µs	−0.0%
array/reductions/reduce/Float32/1d	219 µs	216 µs	−1.0%
array/reductions/reduce/Float32/dims=1	212 µs	212 µs	−0.1%
array/reductions/reduce/Float32/dims=1L	580 µs	576 µs	−0.7%
array/reductions/reduce/Float32/dims=2	253 µs	255 µs	+0.7%
array/reductions/reduce/Float32/dims=2L	422 µs	413 µs	−2.1%
array/reductions/reduce/Int64/1d	233 µs	230 µs	−1.7%
array/reductions/reduce/Int64/dims=1	224 µs	220 µs	−2.0%
array/reductions/reduce/Int64/dims=1L	1.00 ms	999 µs	−0.2%
array/reductions/reduce/Int64/dims=2	262 µs	264 µs	+0.6%
array/reductions/reduce/Int64/dims=2L	590 µs	606 µs	+2.7%
array/shared/copy	128 µs	129 µs	+1.0%
array/shared/copyto!/cpu_to_gpu	36.8 µs	37.5 µs	+1.8%
array/shared/copyto!/gpu_to_cpu	37.3 µs	37.8 µs	+1.5%
array/shared/copyto!/gpu_to_gpu	37.3 µs	37.9 µs	+1.7%
array/shared/iteration/findall/bool	359 µs	359 µs	−0.1%
array/shared/iteration/findall/int	429 µs	429 µs	+0.1%
array/shared/iteration/findfirst/bool	259 µs	278 µs	+7.2%
array/shared/iteration/findfirst/int	286 µs	282 µs	−1.3%
array/shared/iteration/findmin/1d	347 µs	347 µs	−0.0%
array/shared/iteration/findmin/2d	391 µs	396 µs	+1.4%
array/shared/iteration/logical	367 µs	366 µs	−0.2%
array/shared/iteration/scalar	75.7 ns	84.5 ns	+11.6%
array/sorting/1d	1.91 ms	1.91 ms	+0.2%
array/sorting/2d	8.32 ms	8.37 ms	+0.6%
kernel/indexing	216 µs	210 µs	−2.9%
kernel/indexing_checked	393 µs	391 µs	−0.4%
kernel/launch	775 ns	779 ns	+0.5%	noise unknown
kernel/metalcall	821 ns	833 ns	+1.5%	noise unknown
kernel/rand	410 µs	406 µs	−0.8%
metal/synchronization/context	556 ns	572 ns	+2.9%
metal/synchronization/stream	362 ns	369 ns	+2.1%
Latency
compilation	1.78 s	1.77 s	−0.8%
import	1.47 s	1.47 s	+0.4%
launch	1.61 s	1.59 s	−1.0%	noise unknown
precompile	35.3 s	35.4 s	+0.3%
Applications
byval/reference	1.12 ms	1.12 ms	−0.1%
byval/slices=1	1.11 ms	1.12 ms	+0.1%
byval/slices=2	2.03 ms	2.02 ms	−0.4%
byval/slices=3	6.78 ms	6.80 ms	+0.3%
metaldevrt	370 µs	393 µs	+6.1%	🔴 slower

History: https://juliagpu.org/perf/?pkg=metal