isapprox is incorrect for tolerances beyond standard precision

[tobydriscoll]

The following is incorrect:

julia> T = Double64
Double64 (alias for DoubleFloat{Float64})

julia> x = Double64(0.9, 1e-20)
9.00000000000000022214460492503130852e-01

julia> abs(x - T(9)/10)
2.22144604925031320405193304841894479e-17

julia> isapprox(x, T(9)/10; rtol=1e-22, atol=1e-22)
true

If I understand the internals, the isapprox function uses HI(x)===HI(y) as a shortcut for the test, which doesn't look right.

[JeffreySarnoff]

What would you recommend?

…

On Mon, Aug 5, 2024 at 3:07 PM Toby Driscoll ***@***.***> wrote: The following is incorrect: julia> T = Double64 Double64 (alias for DoubleFloat{Float64}) julia> x = Double64(0.9, 1e-20)9.00000000000000022214460492503130852e-01 julia> abs(x - T(9)/10)2.22144604925031320405193304841894479e-17 julia> isapprox(x, T(9)/10; rtol=1e-22, atol=1e-22)true If I understand the internals, the isapprox function uses HI(x)===HI(y) as a shortcut for the test, which doesn't look right. — Reply to this email directly, view it on GitHub <#206>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AAM2VRTX44G3MBTT3DCZMETZP7EORAVCNFSM6AAAAABMA3T4U6VHI2DSMVQWIX3LMV43ASLTON2WKOZSGQ2DSMRYGAYTGNQ> . You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>

[tobydriscoll]

The most straightforward thing would be to remove HI(x) === HI(y) || from line 20 of misc.jl. I suppose you could keep it by pairing it with a test that rtol is large enough, but I'm skeptical that the potential time savings is worth very much.

And then. of course, adding some relevant unit tests. 😁

[JeffreySarnoff]

anyplace that HI(x) is appropriate to be used in place of (x) it should be -- the internals of a full isapprox evaluation in Double64s is more involved .. once that happens is everything tends to intermix and that can extend runtimes (just my experience)

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On Tue, Aug 6, 2024 at 10:13 AM Toby Driscoll ***@***.***> wrote: The most straightforward thing would be to remove HI(x) === HI(y) || from line 20 of misc.jl. I suppose you could keep it by pairing it with a test that rtol is large enough, but I'm skeptical that the potential time savings is worth very much. And then. of course, adding some relevant unit tests. 😁 — Reply to this email directly, view it on GitHub <#206 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AAM2VRRCYWQPILS3KPDE77DZQDKZ5AVCNFSM6AAAAABMA3T4U6VHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZDENZRGQYDEMZTGQ> . You are receiving this because you commented.Message ID: ***@***.***>

[tobydriscoll]

OK, if the HI parts of x and y are the same, then x-y is equal to x.lo-y.lo, right? So that's cheap.

But I don't know if you can cheat on the rtol*max(abs(x), abs(y)) part if rtol is specified in the same precision as x and y. The chances that you would care about the difference between using, say, abs(x) and abs(x.hi) there seem remote, but you can probably invent a pathological counterexample that would break the implied guarantee.