Talk:Sequence of non-squares: Difference between revisions
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:I suggest they choose/use the precision that gives correct results over the stated range, or reduce the range to suit the precision they have and add a comment. I think its true that most languages on Rosetta supporting floating point also support more than 32 bit FP values. --[[User:Paddy3118|Paddy3118]] 11:28, 24 August 2008 (UTC) |
:I suggest they choose/use the precision that gives correct results over the stated range, or reduce the range to suit the precision they have and add a comment. I think its true that most languages on Rosetta supporting floating point also support more than 32 bit FP values. --[[User:Paddy3118|Paddy3118]] 11:28, 24 August 2008 (UTC) |
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== Zero == |
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I thought we were in the realm of Number Theory where [http://en.wikipedia.org/wiki/Natural_number#History_of_natural_numbers_and_the_status_of_zero Wikipedia states] they don't include zero as a natural number, so went with the term Natural Number, but the term Positive Integer ''might'' be more exact. --[[User:Paddy3118|Paddy3118]] 11:36, 24 August 2008 (UTC) |
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Revision as of 11:36, 24 August 2008
I chose this as a way to show how easy it is to investigate functions in a programming language. --Paddy3118 08:42, 24 August 2008 (UTC)
Stability, Accuracy
The formula need to be investigated for numeric stability. Calculation of sqrt is inexact, it need to be shown that for all n in question, floor(1/2 + sqrt(n)) yields the exact result. A minimal requirement for this (though insufficient, I guess) is that sqrt has an error below 0.5. Note that the addition following to squaring will normalize for big n. Also conversion of those to floating point becomes quickly inexact when 32-bit floats are used. --Dmitry-kazakov 09:51, 24 August 2008 (UTC)
- I suggest they choose/use the precision that gives correct results over the stated range, or reduce the range to suit the precision they have and add a comment. I think its true that most languages on Rosetta supporting floating point also support more than 32 bit FP values. --Paddy3118 11:28, 24 August 2008 (UTC)
Zero
I thought we were in the realm of Number Theory where Wikipedia states they don't include zero as a natural number, so went with the term Natural Number, but the term Positive Integer might be more exact. --Paddy3118 11:36, 24 August 2008 (UTC)