[SystemSafety] Accuracy of COVID modeling code

[Olwen Morgan]

I agree that choice of algorithm is much more important than compiler 
optimisations. Indeed, a reliance on compiler optimisations is often, in 
my experience, a sign of underlying ignorance of relevant numerical 
algorithms. This is particularly visible when, using an iterative 
numerical method, one does not pay sufficient - or as is often the case 
absolutely no - attention to getting good starting values. Another 
mortal sin is to forget about strict error bounds. Chebyshev always 
insisted on them and he was one of the founders of modern approximation 
theory.

And as regards summing numbers in ascending order of magnitude, yes, it 
is better than summing them in no particular order, but there still 
pitfalls for the unwary even when ascending order is used. The best 
short text on this is, IMHO:

/Rounding Errors in Algebraic Processes/, J. H. Wilkinson, Dover 
Publications

though it's hard to get hold of and can cost an arm and a leg even when 
you can find it.


regards,

Olwen


On 10/05/2020 15:54, Peter Bishop wrote:
> Exact results are pretty unlikely for FP.
> But on the other hand, I think the *numerical algorithm* is probably 
> more important than any local HLL optimisations in reducing rounding 
> errors,
> e.g. when adding an array of FP numbers, the best option is to sort 
> them an ascending order before sequentially adding them.
>
> Peter Bishop
>
> On 09/05/2020 18:21, Peter Bernard Ladkin wrote:
>> On 2020-05-09 18:41 , Derek M Jones wrote:
>>> Section 5.1.2.3 of the C Standard,
>>>
>>> or sentence 189:https://c0x.coding-guidelines.com/5.1.2.3.html
>>> "In the abstract machine, all expressions are evaluated as specified by the semantics."
>> Which should mean that the expression "x^2 - y^2" returns the square of the value of x minus the
>> square of the value of y. What is called the exact value.
>>
>> What a poor piece of writing.
>>
>> PBL
>>
>> Prof. Peter Bernard Ladkin, Bielefeld, Germany
>> Styelfy Bleibgsnd
>> Tel+msg +49 (0)521 880 7319www.rvs-bi.de
>>
>>
>>
>>
>>
>>
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> -- 
>
> Peter Bishop
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