Inexact numbers as keys in Association?












1












$begingroup$


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.





associations machine-precision







share|improve this question









$endgroup$








  • 1




    $begingroup$
    Looks like this thing, but with associations. Why do you need to use inexact numbers as keys?
    $endgroup$
    – J. M. is slightly pensive♦
    1 hour ago






  • 1




    $begingroup$
    "Can someone explain me how Mathematica's Associations behave [...]?" They behave badly. Don't do that.
    $endgroup$
    – Henrik Schumacher
    1 hour ago


















1












$begingroup$


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.





associations machine-precision







share|improve this question









$endgroup$








  • 1




    $begingroup$
    Looks like this thing, but with associations. Why do you need to use inexact numbers as keys?
    $endgroup$
    – J. M. is slightly pensive♦
    1 hour ago






  • 1




    $begingroup$
    "Can someone explain me how Mathematica's Associations behave [...]?" They behave badly. Don't do that.
    $endgroup$
    – Henrik Schumacher
    1 hour ago
















1












1








1





$begingroup$


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.





associations machine-precision







share|improve this question









$endgroup$




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.





associations machine-precision




associations machine-precision






share|improve this question













share|improve this question











share|improve this question




share|improve this question










asked 1 hour ago









Ali HashmiAli Hashmi

5,69731432




5,69731432








  • 1




    $begingroup$
    Looks like this thing, but with associations. Why do you need to use inexact numbers as keys?
    $endgroup$
    – J. M. is slightly pensive♦
    1 hour ago






  • 1




    $begingroup$
    "Can someone explain me how Mathematica's Associations behave [...]?" They behave badly. Don't do that.
    $endgroup$
    – Henrik Schumacher
    1 hour ago
















  • 1




    $begingroup$
    Looks like this thing, but with associations. Why do you need to use inexact numbers as keys?
    $endgroup$
    – J. M. is slightly pensive♦
    1 hour ago






  • 1




    $begingroup$
    "Can someone explain me how Mathematica's Associations behave [...]?" They behave badly. Don't do that.
    $endgroup$
    – Henrik Schumacher
    1 hour ago










1




1




$begingroup$
Looks like this thing, but with associations. Why do you need to use inexact numbers as keys?
$endgroup$
– J. M. is slightly pensive♦
1 hour ago




$begingroup$
Looks like this thing, but with associations. Why do you need to use inexact numbers as keys?
$endgroup$
– J. M. is slightly pensive♦
1 hour ago




1




1




$begingroup$
"Can someone explain me how Mathematica's Associations behave [...]?" They behave badly. Don't do that.
$endgroup$
– Henrik Schumacher
1 hour ago






$begingroup$
"Can someone explain me how Mathematica's Associations behave [...]?" They behave badly. Don't do that.
$endgroup$
– Henrik Schumacher
1 hour ago












1 Answer
1






active

oldest

votes


















2












$begingroup$

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.






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    $begingroup$

    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.






    share|improve this answer









    $endgroup$


















      2












      $begingroup$

      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.






      share|improve this answer









      $endgroup$
















        2












        2








        2





        $begingroup$

        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.






        share|improve this answer









        $endgroup$



        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.







        share|improve this answer












        share|improve this answer



        share|improve this answer










        answered 1 hour ago









        Daniel LichtblauDaniel Lichtblau

        47.3k276164




        47.3k276164






























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