Inexact numbers as keys in Association?

Question

Can someone explain me how Mathematica's Associations behave with inexact numbers as keys:

<| 0.22499999999999964` -> a |> [0.22499999999999965`]

and

<| 0.22499999999999964` -> a |> [0.22499999999999961`]

both give the value a, whereas

 <| 0.22499999999999964` -> a |> [0.22499999999999966`] gives Missing as an answer.

Looks like this thing, but with associations. Why do you need to use inexact numbers as keys? — J. M.'s missing motivation, Mar 31 '19 at 13:50
"Can someone explain me how Mathematica's Associations behave [...]?" They behave badly. Don't do that. — Henrik Schumacher, Mar 31 '19 at 13:51
Association is the name of the function in Mathematica, so I am not sure what was productive about the edit I just rolled back. — J. M.'s missing motivation, Apr 01 '19 at 06:22

score 10 · Accepted Answer · answered Mar 31 '19 at 13:59

Lookups with inexact numbers behave like other lookups: they use hashing. We can check that the results are consistent with what Hash does.

vals = {0.22499999999999961`, 0.22499999999999964`, 
   0.22499999999999965`, 0.22499999999999966`};
Hash /@ vals

(* Out[11]= {1879126079618645156, 1879126079618645156, \
1879126079618645156, 5861724109654749116} *)

When hashing approximate values, there are going to be sharp boundaries (discontinuities, in effect). This is a tradeoff between having "very" close neighbors hash to the same value, and maintaining transitivity.

Inexact numbers as keys in Association?

1 Answers1