Foreach Range Statement

[Bill Baxter]

Don Clugston wrote:

> OK, that makes sense. Although, for the integer case it's clear how many 
> elements are in a range; it's not at all obvious for floating point.
> 
>>  To have the beginning or end be infinite is asking for trouble.  For 
>> instance in Matlab that tries to allocate an infinite-sized array of 
>> numbers.
> 
> Agreed. Although 0..infinity is only one element bigger than 0..real.max.

Either way, it's still going to be a memory error in Matlab.  The 
real.max one would probably be a memory error in Numpy too.

>>
>> Right.  Numpy had the same problem.  Python itself uses the same 
>> non-inclusive rule as D. But Python only handles integers in things 
>> like the "range(start,end,step)" function.  The Numpy folks wanted to 
>> extend that to work for floating point types as well.  But actually, 
>> in both matlab and numpy, if you want an evenly spaced set of numbers, 
>> you usually use the 'linspace' function, which has the signature 
>> linspace(begin,end,numvals).  This creates an inclusive array of numbers.
> 
> That makes sense. You could also have a logarithmic range.

Yes, both have a "logspace" function as well.

> But what need is there for using ".." with floating point numbers? 
> Surely we can already write
> foreach(float x, linspace(begin, end, numvals)){}

I can't really think of any super duper reason.  It's just a shortcut for:
   for(float x=0.0; x<end; x+=0.1) { }

I've used it in Python before.  I think I used it more in Matlab, 
though, where the ranges are inclusive.

>> I think one source of confusion is that ranges and slices are very 
>> similar things, but not quite the same.
>>
>> * A range is just a sequence of numbers.  It can exist and be 
>> interpreted independently.  Here allowing floating point numbers makes 
>> sense.  Allowing for infinity may make sense, but practically it's 
>> very niche.  Iterating over infinite things usually takes either too 
>> much time or too much memory.
> 
> How is that different to a set? I've always assumed a range (a,b) 
> contained EVERYTHING between a and b. I'm not very familiar with either 
> Python or Matlab.

Yes. It is just a set.  An ordered set with fixed spacing between 
elements, expressed using a compact notation.

>> * A slice needs an object to operate on for interpretation of 
>> object-relative things like $.  Generally speaking, only integers make 
>> sense in a slice.  Infinity doesn't really make sense because you 
>> can't generally have things that are both slice-able and infinite on a 
>> computer.
>>
>> (* An interval just represents two points on a numberline, plus maybe 
>> an indication of the inclusivity of the endpoints.  Infinity -- ok. 
>> Floating point -- ok.)
>>
>> It may be possible to combine the concepts into one type, but they 
>> *are* slightly different, and may benefit from being treated as so.
> 
> That clarification is very helpful. Thanks.

--bb