Configurable tolerance for numerical equality?

Question

In standard C++ the double values for 1. + 1.2*^-16 and 1. are not considered equal. But in Mathematica, I get the following:

With[{aux = 1 + 1.2*^-16}, 
 {{1 == aux, 1. == aux}, {1 < aux, 1. < aux}, {ArcSin[aux], ArcSin[1.]}}]

returns

{{True, True}, {False, False}, {1.5708 - 2.10734*10^-8 I, 1.5708}}

Is there a parameter that I can set, to get the behaviour as in C++, i.e. strict floating point equality?

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score 7 · Accepted Answer · edited May 23 '17 at 12:35

7

See How to make the computer consider two numbers equal up to a certain precision and the linked SO answer for more details. This question is similar to the first one, except the OP here wants the tolerance to be $-\infty$, instead of greater.

Block[{Internal`$EqualTolerance = -∞},
 1 + $MachineEpsilon == 1.
 ]
1 + $MachineEpsilon == 1.
(*
  False
  True
*)

edited May 23 '17 at 12:35

Community

answered Feb 28 '16 at 14:34

Michael E2

2

Perhaps this question should be considered a duplicate? – Michael E2 Feb 28 '16 at 14:36
2

For zero bits tolerance, Internal\$EqualToleranceshould be-Infinity. A value of0` leaves 1 bit tolerance. – Oleksandr R. Feb 28 '16 at 18:28
@OleksandrR. Thanks. I misremembered how it works. – Michael E2 Feb 28 '16 at 18:30

1 Answers1