std.range.iota enhancement: supporting more types (AKA issue 10762)

[Andrei Alexandrescu]

On 12/24/13 11:59 AM, H. S. Teoh wrote:
> On Tue, Dec 24, 2013 at 11:35:49AM -0800, Andrei Alexandrescu wrote:
>> On 12/24/13 10:56 AM, Craig Dillabaugh wrote:
>>> On Tuesday, 24 December 2013 at 17:10:53 UTC, Andrei Alexandrescu
>>> wrote:
> [.[..]
>>>> The integral cases are easy. We need to crack the floating point
>>>> case: given numbers low, up, and step, what's the closest number
>>>> smaller than up that's reached by repeated adds of step to low?
>>>>
>>>> Andrei
>>>
>>> Doesn't think work, or am I missing something?
>>>
>>> low + floor( (up-low)/step ) * step
>>
>> I doubt it's anything as simple as that. The magnitudes of up, low,
>> and step must be taken into account.
> [...]
>
> What about low + fmod(up-low, step)*step? Is that better? (Assuming that
> fmod would take relative magnitudes into account, of course.)

No, again, I think nothing like that would work. It's hopelessly naive 
(in addition to being plain wrong for simple inputs like low=1, high=10, 
step=1).

There are combinations of low, high, and step that don't even make 
progress, i.e. step is sufficiently small compared to low to effectively 
make low + step == low.

Try this to verify approaches:

#!/Users/aalexandre/bin/rdmd
import std.stdio, std.conv, std.math;

void main(string[] args)
{
     auto low = to!double(args[1]);
     auto up = to!double(args[2]);
     auto step = to!double(args[3]);
     writeln("Predicted: ", low + fmod(up-low, step)*step);
     for (;;)
     {
         auto next = low + step;
         if (next >= up) break;
         low = next;
     }
     writeln("Actual: ", low);
}


Andrei