Re: Motion 46: finalise interval literals, amendments
On 2013-06-23, at 10:21 PM, Jürgen Wolff von Gudenberg <wolff@xxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote:
> p1788 SHALL prescribe the strings that are valid inputs for text2intval
By text2interval, I would consider only converting a string to an interval, not two strings that represent an
interval to an interval. So, we can assume the same syntax of a string as let's say what C or Fortran assumes.
Ned
> it Shall NOT give rules for specification of how interval literals may be written in any languag implementation.
> A recommendation that the language should introduce the corresponding syntax rules is ok
>
> Jürgen
>
>
>> John Pryce
>>
>> ---------------------------------------------
>> On 10 Jun 2013, at 19:55, Ian McIntosh wrote:
>>> More conversion functions than just text2interval are needed.
>>>
>>> One function would convert a single precision value and another a double precision value, both with a parameter specifying how precise they should be considered.
>>> You could write
>>> float x = 0.1f;
>>> interval a = float2interval (x, 7);
>>> to say that x should be considered to have 7 significant digits (0.1f happens to be accurate to 8 digits), and
>>> double y = 0.1;
>>> interval b = double2interval (y, 16);
>>> to assert 16 digit accuracy for y.
>>
>> Can you give an application where it would be useful? And a pitfall the user might fall into if she writes it herself, e.g. (in Matlab style) as follows?
>>
>> function a = float2interval(x,d)
>> xerr = x/10^d;
>> a = nums2interval(x-xerr,x+xerr);
>> end
>>
>>> For text conversions, there are arguments in favour of two different semantics. In one, "0.1" and "0.100000" are considered as identical infinitely precise representations of 1/10. In the other, "0.1" and "0.100000" are considered as different, with "0.1" meaning [0.05, 0.15] and "0.100000" meaning [0.0000005, 0.1000005]. The first is useful for the mathematical value 1/10, and the second is more useful for measured values where trailing zeros indicate how precise the measurement was. A mathematician who wrote that only the first is needed and an engineer who said only the second is convinced me that both are. 8<)
>>
>> Sun offers both, and so does the proposed 1788 scheme. Here is code example 2-37 from 2.10.2.3 of Sun Interval Fortran Reference. I have prefixed lines of input with <1>, <2>, etc. for ease of reference, and the next line is the output produced. I put comments giving the P1788 version of the input.
>>
>> math% cat ce2-37.f95
>> INTERVAL, DIMENSION(6) :: X
>> INTEGER I
>> DO I = LBOUND(X, 1), UBOUND(X, 1)
>> READ(*, *) X(I)
>> WRITE(*, *) X(I)
>> END DO
>> END
>> math% f95 -xia ce2-37.f95
>> math% a.out
>> <1> 1.234500 !P1788 says "1.234500?1"
>> [1.2344989999999997,1.2345010000000001]
>> <2> [1.2345] !proposed that P1788 says same as Sun
>> [1.2344999999999999,1.2345000000000002]
>> <3> [-inf,2] !P1788 says same as Sun
>> [-Inf,2.0]
>> <4> [-inf] !not valid in P1788
>> [-Inf,-1.7976931348623157E+308]
>> <5> [EMPTY] !currently P1788 says "EMPTY", no brackets
>> [EMPTY]
>> <6> [1.2345,1.23456] !P1788 says same as Sun
>> [1.2344999999999999,1.2345600000000002]
>>
>> For comparisons, assume the "same" P1788 interval type is used, i.e. infsup binary64.
>>
>> <1> shows Ian's "other semantics". 1.234500 denotes the exact interval [1.234499, 1.234501] and Sun encloses this in the tightest representable interval. P1788 can do the same, with slightly different notation.
>>
>> <2,3,6> are as expected. Well, as I expect. I continue to think Richard Fateman has it wrong, and Sun has it right. An exact mathematical interval is formed and enclosed in the tightest representable interval.
>>
>> <5>. I think Sun is right here and we should use [EMPTY], not EMPTY.
>>
>> <4> is interesting. This is basically Siegfried Rump's proposal that *in this context only* -- a single point interval -- inf should be regarded as "a large unknown finite number", so it defines a nonempty (but unknown) interval.
>> Then its Level 2 hull is [REALMAX,oo] (or [HUGEPOS,oo], in the notation of 11.11.8 "Constructors"). I already put this idea into the definition of nums2interval(). Should it be in text2interval()?
>>
>
> --
> o Prof. Dr. Juergen Wolff von Gudenberg, Lehrstuhl fuer Informatik II
> / \ Universitaet Wuerzburg, Am Hubland, D-97074 Wuerzburg
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