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Inexact numbers as keys in Association?

4

$begingroup$

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

edited Apr 1 at 6:21

J. M. is away♦

98.9k10311467

asked Mar 31 at 13:38

Ali HashmiAli Hashmi

5,73931433

$endgroup$

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  Looks like this thing, but with associations. Why do you need to use inexact numbers as keys?
  $endgroup$
  – J. M. is away♦
  Mar 31 at 13:50
  

  
  
  
  


• 
  
  
  

  
  4
  

  
  
  
  
  
  

  
  $begingroup$
  "Can someone explain me how Mathematica's Associations behave [...]?" They behave badly. Don't do that.
  $endgroup$
  – Henrik Schumacher
  Mar 31 at 13:51
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Association is the name of the function in Mathematica, so I am not sure what was productive about the edit I just rolled back.
  $endgroup$
  – J. M. is away♦
  Apr 1 at 6:22
  

  
  
  
  

add a comment | 

4

$begingroup$

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

edited Apr 1 at 6:21

J. M. is away♦

98.9k10311467

asked Mar 31 at 13:38

Ali HashmiAli Hashmi

5,73931433

$endgroup$

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  Looks like this thing, but with associations. Why do you need to use inexact numbers as keys?
  $endgroup$
  – J. M. is away♦
  Mar 31 at 13:50
  

  
  
  
  


• 
  
  
  

  
  4
  

  
  
  
  
  
  

  
  $begingroup$
  "Can someone explain me how Mathematica's Associations behave [...]?" They behave badly. Don't do that.
  $endgroup$
  – Henrik Schumacher
  Mar 31 at 13:51
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Association is the name of the function in Mathematica, so I am not sure what was productive about the edit I just rolled back.
  $endgroup$
  – J. M. is away♦
  Apr 1 at 6:22
  

  
  
  
  

add a comment | 

$begingroup$

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

edited Apr 1 at 6:21

J. M. is away♦

98.9k10311467

asked Mar 31 at 13:38

Ali HashmiAli Hashmi

5,73931433

$endgroup$

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

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

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

share|improve this question

edited Apr 1 at 6:21

J. M. is away♦

98.9k10311467

asked Mar 31 at 13:38

Ali HashmiAli Hashmi

5,73931433

share|improve this question

edited Apr 1 at 6:21

J. M. is away♦

98.9k10311467

asked Mar 31 at 13:38

Ali HashmiAli Hashmi

5,73931433

edited Apr 1 at 6:21

J. M. is away♦

98.9k10311467

edited Apr 1 at 6:21

J. M. is away♦

98.9k10311467

asked Mar 31 at 13:38

Ali HashmiAli Hashmi

5,73931433

asked Mar 31 at 13:38

Ali HashmiAli Hashmi

5,73931433

1 Answer
1

active

oldest

votes

10

$begingroup$

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

answered Mar 31 at 13:59

Daniel LichtblauDaniel Lichtblau

47.6k277165

$endgroup$

add a comment | 

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10

$begingroup$

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

answered Mar 31 at 13:59

Daniel LichtblauDaniel Lichtblau

47.6k277165

$endgroup$

add a comment | 

10

$begingroup$

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

answered Mar 31 at 13:59

Daniel LichtblauDaniel Lichtblau

47.6k277165

$endgroup$

add a comment | 

$begingroup$

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

answered Mar 31 at 13:59

Daniel LichtblauDaniel Lichtblau

47.6k277165

$endgroup$

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

(* Out[11]= 1879126079618645156, 1879126079618645156, 
1879126079618645156, 5861724109654749116 *)

share|improve this answer

answered Mar 31 at 13:59

Daniel LichtblauDaniel Lichtblau

47.6k277165

answered Mar 31 at 13:59

Daniel LichtblauDaniel Lichtblau

47.6k277165

answered Mar 31 at 13:59

Daniel LichtblauDaniel Lichtblau

47.6k277165