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float16 cbrt, 50% faster #39441

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merged 4 commits into from
Apr 17, 2021
Merged

float16 cbrt, 50% faster #39441

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ef720bf
float16 cbrt, 50% faster
oscardssmith Jan 28, 2021
a8ad312
fix
oscardssmith Jan 28, 2021
a5b7e73
fix whitespace
oscardssmith Feb 1, 2021
430b64d
Update base/special/cbrt.jl
KristofferC Feb 17, 2021
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17 changes: 17 additions & 0 deletions base/special/cbrt.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -147,3 +147,20 @@ function cbrt(x::Union{Float32,Float64})
t = _approx_cbrt(x)
return _improve_cbrt(x, t)
end

function cbrt(a::Float16)
if !isfinite(a) || iszero(a)
return a
end
x=Float32(a)
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# 5 bit approximation. Simpler than _approx_cbrt since subnormals can not appear
u = highword(x) & 0x7fff_ffff
v = div(u, UInt32(3)) + 0x2a5119f2
t = copysign(fromhighword(Float32, v), x)

# 2 newton iterations
t = 0.33333334f0 * (2f0*t + x/(t*t))
t = 0.33333334f0 * (2f0*t + x/(t*t))
return Float16(t)
end