Timeline for How does Internal`CompareNumeric work?
Current License: CC BY-SA 3.0
18 events
| when toggle format | what | by | license | comment | |
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| Apr 3, 2017 at 10:22 | history | edited | TimRias | CC BY-SA 3.0 |
Correct machineprecision behavior
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| Apr 3, 2017 at 9:29 | history | edited | TimRias | CC BY-SA 3.0 |
code typo
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| Apr 3, 2017 at 7:14 | comment | added | TimRias |
@xzczd It is indeed the case that the absolute tolerance ε is no longer 10^(-$MachinePrecision/2) in that case. But the "effective precision" ep as it appears in the mock function is still $MachinePrecision/2. That is where the division by Abs[a]+Abs[b] comes in. (Actually I've found that it is not quite $MachinePrecision/2, but somewhere close to that, i.e. within 1%.
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| Apr 3, 2017 at 7:09 | history | edited | TimRias | CC BY-SA 3.0 |
Divide by |a|+|b| instead of |a+b|, see comments
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| Apr 2, 2017 at 7:44 | comment | added | xzczd♦ |
I'm afraid the guess ε = 10^(-$MachinePrecision/2) is incorrect, if you modify tf to tf[tol_?NumericQ, prec_?NumericQ, digit_?NumericQ] := Internal`CompareNumeric[tol, SetPrecision[100, prec], SetPrecision[100, prec] + 10^-SetPrecision[digit, 100]], you will find the split digit seems to become $MachinePrecision/2 - 2
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| Mar 30, 2017 at 11:37 | comment | added | TimRias | Note that the mock function easily reproduces the odd behavior observed in the other answers. | |
| Mar 30, 2017 at 11:34 | history | edited | TimRias | CC BY-SA 3.0 |
addendum on what this means
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| Mar 30, 2017 at 11:11 | comment | added | TimRias | @Shadowray: I guess the denominator may need to be Abs[a]+Abs[b] rather than Abs[a+b] | |
| Mar 30, 2017 at 11:09 | history | edited | TimRias | CC BY-SA 3.0 |
x -> p
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| Mar 30, 2017 at 9:36 | comment | added | Ray Shadow |
What if one evaluates MockCompareNumeric[5, -0.9252872333493522561`2., 0.9289648686205458361`3.] ?
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| Mar 30, 2017 at 8:58 | history | edited | TimRias | CC BY-SA 3.0 |
mock function
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| Mar 29, 2017 at 16:07 | history | edited | xzczd♦ | CC BY-SA 3.0 |
added 5 characters in body
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| Mar 29, 2017 at 14:06 | comment | added | TimRias |
@ J.M. Ah, I see. Well, in this case we are not interested in finding the threshold where the two numbers are no longer considered the "same" by Internal`CompareNumeric which is a slightly different question, than find the threshold where the internal representation becomes the same. (Arbitrary precision numbers in Mathematica can have many more digits in their internal representation than their actual precision value.)
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| Mar 29, 2017 at 13:58 | comment | added | J. M.'s missing motivation♦ | You mentioned wanting to find the threshold value where two numbers are no longer the same, so I think a function that would give the "next" floating point number might suit your needs. | |
| Mar 29, 2017 at 13:55 | comment | added | TimRias | @ J.M. No I hadn't. I am also not sure why you are pointing to it. Could you explain? | |
| Mar 29, 2017 at 13:46 | history | edited | TimRias | CC BY-SA 3.0 |
finish premature post
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| Mar 29, 2017 at 13:25 | comment | added | J. M.'s missing motivation♦ | Have you seen this, by any chance? | |
| Mar 29, 2017 at 13:21 | history | answered | TimRias | CC BY-SA 3.0 |