Convert `ArbFloat` to `Float32` gives wrong results

[inkydragon]

When I'm trying to use ArbFloat to replace BigFloat...

julia> x = Float32(0.00024868647)
0.00024868647f0

julia> acos(x)
1.5705476f0

julia> acos(BigFloat(x)) |> Float32
1.5705477f0

julia> acos(ArbFloat(x)) |> Float32
1.5705476f0

But y=acos(x) is closed to hi=1.5705477f0

julia> x
0.00024868647f0

julia> y = acos(ArbFloat(x))
1.570547640323638925989674629263948326250377240078317

julia> lo, hi = ArbFloat(1.5705476f0), ArbFloat(1.5705477f0)
(1.570547580718994140625, 1.57054769992828369140625)

julia> (lo==Float32(y), hi==Float32(y))
(true, false)

julia> abs(lo-y) > abs(y-hi)
true

Another example:

julia> x = 1.5893255f-8
1.5893255f-8

julia> acos(x)
1.5707963f0

julia> acos(BigFloat(x)) |> Float32
1.5707964f0

julia> acos(ArbFloat(x)) |> Float32
1.5707963f0

[JeffreySarnoff]

According to WolframAlpha <https://www.wolframalpha.com/input?i=acos%280.00024868647%29> acos(0.00024868647) is 1.57054764032..

…

On Wed, May 21, 2025 at 9:19 AM Chengyu Han ***@***.***> wrote: *inkydragon* created an issue (JeffreySarnoff/ArbNumerics.jl#85) <#85> When I'm trying to use ArbFloat to replace BigFloat... julia> x = Float32(0.00024868647)0.00024868647f0 julia> acos(x)1.5705476f0 julia> acos(BigFloat(x)) |> Float321.5705477f0 julia> acos(ArbFloat(x)) |> Float321.5705476f0 But y=acos(x) is closed to hi=1.5705477f0 julia> x0.00024868647f0 julia> y = acos(ArbFloat(x))1.570547640323638925989674629263948326250377240078317 julia> lo, hi = ArbFloat(1.5705476f0), ArbFloat(1.5705477f0) (1.570547580718994140625, 1.57054769992828369140625) julia> (lo==Float32(y), hi==Float32(y)) (true, false) julia> abs(lo-y) > abs(y-hi)true — Reply to this email directly, view it on GitHub <#85>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AAM2VRX2GC4OJSGSPEO3JN327R4OZAVCNFSM6AAAAAB5TITH5WVHI2DSMVQWIX3LMV43ASLTON2WKOZTGA4DAMRRHEZTCMI> . You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>

[JeffreySarnoff]

Also note ``` julia> x = Float32(0.00024868647) 0.00024868647f0 julia> acos(x) 1.5705476f0 julia> Float32(acos(Float64(x))) 1.5705476f0 ``` On Thu, May 22, 2025 at 7:31 AM Jeffrey Sarnoff ***@***.***> wrote:

…

According to WolframAlpha <https://www.wolframalpha.com/input?i=acos%280.00024868647%29> acos(0.00024868647) is 1.57054764032.. On Wed, May 21, 2025 at 9:19 AM Chengyu Han ***@***.***> wrote: > *inkydragon* created an issue (JeffreySarnoff/ArbNumerics.jl#85) > <#85> > > When I'm trying to use ArbFloat to replace BigFloat... > > julia> x = Float32(0.00024868647)0.00024868647f0 > > julia> acos(x)1.5705476f0 > > julia> acos(BigFloat(x)) |> Float321.5705477f0 > > julia> acos(ArbFloat(x)) |> Float321.5705476f0 > > But y=acos(x) is closed to hi=1.5705477f0 > > julia> x0.00024868647f0 > > julia> y = acos(ArbFloat(x))1.570547640323638925989674629263948326250377240078317 > > julia> lo, hi = ArbFloat(1.5705476f0), ArbFloat(1.5705477f0) > (1.570547580718994140625, 1.57054769992828369140625) > > julia> (lo==Float32(y), hi==Float32(y)) > (true, false) > > julia> abs(lo-y) > abs(y-hi)true > > — > Reply to this email directly, view it on GitHub > <#85>, or > unsubscribe > <https://github.com/notifications/unsubscribe-auth/AAM2VRX2GC4OJSGSPEO3JN327R4OZAVCNFSM6AAAAAB5TITH5WVHI2DSMVQWIX3LMV43ASLTON2WKOZTGA4DAMRRHEZTCMI> > . > You are receiving this because you are subscribed to this thread.Message > ID: ***@***.***> >

[JeffreySarnoff]

Additionally, although it does affect your question, BigFloats have a default precision of 256, to give ArbFloats a similar precision use `setprecision(ArbFloats, 256)`; ArbNumerics works hard to ensure all the digits you see are correct. On Thu, May 22, 2025 at 7:33 AM Jeffrey Sarnoff ***@***.***> wrote:

…

Also note ``` julia> x = Float32(0.00024868647) 0.00024868647f0 julia> acos(x) 1.5705476f0 julia> Float32(acos(Float64(x))) 1.5705476f0 ``` On Thu, May 22, 2025 at 7:31 AM Jeffrey Sarnoff ***@***.***> wrote: > According to WolframAlpha > <https://www.wolframalpha.com/input?i=acos%280.00024868647%29> acos(0.00024868647) > is 1.57054764032.. > > > > On Wed, May 21, 2025 at 9:19 AM Chengyu Han ***@***.***> > wrote: > >> *inkydragon* created an issue (JeffreySarnoff/ArbNumerics.jl#85) >> <#85> >> >> When I'm trying to use ArbFloat to replace BigFloat... >> >> julia> x = Float32(0.00024868647)0.00024868647f0 >> >> julia> acos(x)1.5705476f0 >> >> julia> acos(BigFloat(x)) |> Float321.5705477f0 >> >> julia> acos(ArbFloat(x)) |> Float321.5705476f0 >> >> But y=acos(x) is closed to hi=1.5705477f0 >> >> julia> x0.00024868647f0 >> >> julia> y = acos(ArbFloat(x))1.570547640323638925989674629263948326250377240078317 >> >> julia> lo, hi = ArbFloat(1.5705476f0), ArbFloat(1.5705477f0) >> (1.570547580718994140625, 1.57054769992828369140625) >> >> julia> (lo==Float32(y), hi==Float32(y)) >> (true, false) >> >> julia> abs(lo-y) > abs(y-hi)true >> >> — >> Reply to this email directly, view it on GitHub >> <#85>, or >> unsubscribe >> <https://github.com/notifications/unsubscribe-auth/AAM2VRX2GC4OJSGSPEO3JN327R4OZAVCNFSM6AAAAAB5TITH5WVHI2DSMVQWIX3LMV43ASLTON2WKOZTGA4DAMRRHEZTCMI> >> . >> You are receiving this because you are subscribed to this thread.Message >> ID: ***@***.***> >> >