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Re: C language binding of P1888 operations, especially min and max
The attached pages from Sun/Oracle's documentation for its Fortran implementation of interval data types might be informative. 

See below.

On 10/6/13 4:50 PM, Richard Fateman wrote:

On 10/6/2013 1:03 PM, Michel Hack wrote:

So for each "k", it is necessary 2^(k+1) variants.
This is a combinatoric explosure.
How can I bind this in C ?

Input arguments can be widened to the widest-supported type. This avoids
combinatorial explosion; you only need one function per target type.
Several functions, including min/max, don't involve rounding, so you can
generate a wide result and round it once to the target type.
Functions like min/max are often expressed as macros in C, again avoiding type issues. Indeed, macros using the compile-time built-in typeof() can 
provide the appearance of polymorphism.

Michel.
---Sent: 2013-10-06 20:09:50 UTC
I think it is a mistake to require min or max of k arguments except for k=2. 

Presumably the macro expansion that Michel suggests requires only
max2(a,b),   and

max(a,b,c,d)  would be expanded to  max2(a,max2(b,max2(c,d))) etc.
Some languages will support the k-ary version, but why should the standard 
require languages to do so?  Perhaps thereby excluding FORTRANs that may
still be in use.
The Sun/Oracle Fortran implementation supports both more than 2 arguments and array arguments.
If it is used in the form x := max(a,b) and the types of a,b,x are all different, 
do we (in effect) convert them all to the type of x to do the comparison?
Does it even matter unless there is overflow in conversion?
The Sun/Oracle Fortran implementation uses widest need expression evaluation to fully support mixed interval type expressions, wherein every non-interval is promoted to a containing interval with the highest kind-type-parameter-value (ktpv) prior to interval evaluation of the given expression. 

I would expect that if a,b are intervals, that
the return value of max(a,b) is either the memory location where a is stored or where b is stored. Not another location where there is a conversion of a or b 
to the type of x.  But frankly I don't know what is intended here.
Containment sets resolve any ambiguity about the mathematical definition of what must be contained in the interval evaluation of any expression or function. 

Equality has an issue too.
If we compute max(A,B) where A and B are structures which are intervals, and they are of the same type and have equal components, and max returns a pointer to one of them, which one? I suspect this can affect the efficiency of (say) 
an implementation of heapsort.  Also, if they are equal because they are
stored in the same location, what does max say,  even if A=B=NAI.
See the definition of a containment set and the assignment statement operator. 



So there are two items in this message:

1. How about just   max_of_two_arguments(x1,x2)   etc for min
Unnecessarily limited. However, I strongly support a permissive interval standard in which the *only* requirement is to not violate the containment constraint. Thus, any language implementation should be permitted to implement the interval syntax and semantics of the interval evaluation of any standard function in any way, provided only that containment not be violated. 

This is so elegant and so simple. :)


2. What really is returned?
Any interval enclosure of the given function's containment set. Speed and width are quality of implementation features. 

Apologies if I am missing something that is already resolved.

On the contrary, you raise important and fundamental questions.

Cheers,

Bill



RJF

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