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Test BFloat16 arithmetic against exactly rounded references #952

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Merged
maleadt merged 1 commit into from
Nov 6, 2026
Merged

Test BFloat16 arithmetic against exactly rounded references #952

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17 changes: 12 additions & 5 deletions test/bfloat16.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -35,9 +35,16 @@ end
@inbounds y[i] = convert(eltype(y), x[i])
end

# the correctly rounded value, computed without the host's `BFloat16` conversions (on Julia
# 1.11, vectorized ones crash LLVM on AVX512-BF16 hosts)
bf16_nearest(x) = BFloat16(Float32(BigFloat(x; precision = 8)))
# the correctly rounded value, without relying on the host's `BFloat16` rounding: on Julia
# 1.11, vectorized ones crash LLVM on AVX512-BF16 hosts, and LLVM 19 to 22 (Julia 1.13) rounds
# ties wrongly in vectorized ones for AArch64 targets without BF16 (#949)
function bf16_nearest(x)
b = BigFloat(x; precision = 256)
# 8 significant bits, except for subnormals, which are multiples of 2^-133
r = abs(b) < floatmin(Float32) ? round(b * big(2.0)^133) / big(2.0)^133 :
BigFloat(b; precision = 8)
return BFloat16(Float32(r))
end

const bf16_supported = !isdefined(Core, :BFloat16) ||
"SPV_KHR_bfloat16" in POCL.device().spirv_extensions
Expand Down Expand Up @@ -71,7 +78,7 @@ if bf16_supported
a = BFloat16(1.5)
bf16_axpy!(backend)(out, a, x; ndrange = n)
# widened to `float`, multiplied and added separately (each rounded to bfloat)
@test isequal(Array(out), map((x, y) -> BFloat16(Float32(BFloat16(Float32(a) * Float32(x))) + Float32(y)), hx, hy))
@test isequal(Array(out), map((x, y) -> bf16_nearest(Float32(bf16_nearest(Float32(a) * Float32(x))) + Float32(y)), hx, hy))
end

@testset "arithmetic" begin
Expand All @@ -80,7 +87,7 @@ if bf16_supported
o = Array(out)
# (references in `Float32`: on Julia 1.11, the host miscompiles vectorized `BFloat16`
# operations such as `copysign`)
f32(op) = (xs...) -> BFloat16(op(Float32.(xs)...))
f32(op) = (xs...) -> bf16_nearest(op(Float32.(xs)...))
@test isequal(o[1, :], map(f32(/), hx, hy))
@test isequal(o[2, :], map(f32(-), hx, hy))
@test isequal(o[3, :], map(f32(min), hx, hy))
Expand Down
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